Optical system and optical apparatus including optical system

ABSTRACT

An optical system includes a first optical element and a second optical element on at least one of an enlargement side and a reduction side relative to a point P at which a light axis and a paraxial chief ray intersect. Each of the first optical element and second optical element is composed of a solid material having a refractive light incident surface and a refractive light emergent surface. The optical system satisfies the following conditional expressions: ΔθgF1&gt;0.0272, ΔθgF2&lt;−0.0278, and f1×f2&lt;0 where ΔθgF1 and ΔθgF2 denote anomalous partial dispersion values of the first and second optical elements for the g-line and F-line, respectively, and f1 and f2 denote focal lengths of the first and second optical elements, respectively, when the light incident surfaces and the light emergent surfaces of the first and second optical elements are in contact with air.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an optical system and, in particular,an optical system suitable for optical apparatuses, such assilver-halide film cameras, digital still cameras, video cameras,digital video cameras, telescopes, binoculars, projectors, and copyingmachines.

2. Description of the Related Art

Optical systems used for optical apparatuses, such as digital camerasand video cameras, need to have a short total lens length (opticallength: the length between the first lens surface on the object side andthe image plane) and the short length of the optical systems. Ingeneral, as the size of an optical system decreases, the aberrationsand, in particular, the axial chromatic aberration and the chromaticaberration of magnification of the optical system significantlyincrease. Thus, the optical performance of the optical system decreases.

In telephoto optical systems having a short total lens length, as thefocal length increases, chromatic aberration increases. A telephotooptical system that corrects the chromatic aberration by using ananomalous partial dispersion material is described in, for example, U.S.Pat. No. 4,241,983, U.S. Pat. No. 4,348,084, and U.S. Pat. No.6,115,188.

In addition, retrofocus optical systems are known that have a shortfocal length and a long back focus of the optical system. In aretrofocus optical system, a lens group having a negative refractivepower is disposed in the front portion of the optical system (on theobject side for photo-taking lens systems, such as cameras, and on ascreen side (an enlargement side) for projection optical systems, suchas projectors). In addition, a lens group having a positive refractivepower is disposed in the rear portion of the optical system (on theimage side for photo-taking lens systems, such as cameras, and on anoriginal image side (a reduction side) for projection optical systems,such as projectors). Using such a structure, an optical system having along back focus can be achieved.

However, retrofocus optical systems have an asymmetric refractive powerarrangement with respect to an aperture stop. Thus, a negativedistortion aberration (barrel distortion aberration) and chromaticaberration of magnification tend to occur. To correct the chromaticaberration of magnification of retrofocus optical systems, an anomalouspartial dispersion material, such as fluorite, is used for a lens groupon the reduction side, in which a height at which a paraxial chief raypasses through the lens surface from the light axis is relatively high(refer to, for example, Japanese Patent Laid-Open Nos. 06-082689 and2002-287031).

In addition, the chromatic aberration of magnification of opticalsystems can be corrected using a liquid material having a highdispersion characteristic and an anomalous partial dispersioncharacteristic (refer to, for example, U.S. Pat. Nos. 4,913,535 and5,731,907).

Furthermore, the chromatic aberration of magnification of opticalsystems can be corrected using a solid material composed of a mixture ofa transparent material and indium tin oxide (ITO) fine particlesdispersed therein (refer to, for example, U.S. Pat. Nos. 7,136,237,7,057,831, and 7116497).

Still furthermore, the chromatic aberration of magnification of opticalsystems can be corrected using a solid material composed of a mixture ofa transparent material and TiO₂ fine particles dispersed therein or asolid material made of resin (refer to, for example, U.S. Pat. Nos.7,193,789, 7,164,544, and 2007/0014025).

The optical systems using fluorite for the optical material and having arelatively large lens length can be easily corrected for chromaticaberration of magnification. However, as the lens length decreases,occurrence of chromatic aberration of magnification significantlyincreases. It is difficult to sufficiently correct such a chromaticaberration. This is because chromatic aberration occurring in a frontlens unit of a telephoto optical system having a positive refractivepower or chromatic aberration occurring in a lens unit of a retrofocusoptical system disposed closer to the reduction side than the aperturestop and having a positive refractive power is simply reduced by using alow dispersion characteristic and an anomalous partial dispersioncharacteristic of the material of the lens, such as fluorite.

For example, for a fluorite lens using low-dispersion glass having alarge Abbe number, in order to correct chromatic aberration that isincreased by reducing the length of the optical system, the refractivepower of the lens surface needs to be significantly changed. However, ifthe refractive power of the lens surface is significantly changed, avariety of aberrations, such as spherical aberration, coma aberration,and astigmatism aberration, occur. Accordingly, it is difficult tocorrect chromatic aberration and other aberrations at the same time. Inaddition, the fabrication of a glass material having an anomalouspartial dispersion characteristic (such as fluorite) is significantlydifficult. Furthermore, since the surface of the glass material iseasily damaged, the usage of the glass material is limited for someparts of the optical system.

Since the materials described in U.S. Pat. Nos. 4,913,535 and 5,731,907are liquid, a structure to enclose the materials is needed. Thus, whenthese materials are used for an optical system, the fabrication of theoptical system is difficult. In addition, characteristics, such as theindex of refraction and dispersion significantly vary with a change intemperature, and therefore, the resistance to the surroundingenvironment is not sufficient. Furthermore, since the interface with aircannot be obtained, it is difficult to sufficiently correct chromaticaberration.

The transmittance of the solid material having an anomalous partialdispersion characteristic by dispersing ITO fine particles or TiO₂ fineparticles in a transparent material is relatively low, compared with awidely used optical material. To prevent a decrease in transmittance ofthe entire optical system, it is desirable that the thickness of thesolid material in the light axis direction is reduced. However, in orderto sufficiently correct chromatic aberration using the solid material, acertain thickness is required. As the thickness of the solid material inthe optical path increases, variation in the optical performanceincreases in the use environment. Thus, the resistance to thesurrounding environment deteriorates. In addition, it is difficult tomold a thick solid material. Accordingly, the fabrication of an opticalsystem is not easy. Therefore, when an optical element composed of asolid material having an anomalous partial dispersion characteristic isused for a lens or a layer having a refractive power in an opticalsystem, it can be useful that chromatic aberration is corrected whilereducing the thickness of the optical element in the light axisdirection.

SUMMARY OF THE INVENTION

The present invention is directed to an optical system that cansufficiently correct a variety of aberrations including chromaticaberration, that can be easily fabricated, and that has an excellentresistance to the surrounding environment, and an optical apparatusincluding the optical system.

According to an embodiment of the present invention, an optical systemincludes a first optical element and a second optical element on atleast one of an enlargement side and a reduction side relative to apoint P at which a light axis and a paraxial chief ray intersect. Eachof the first optical element and second optical element includes a solidmaterial having a refractive light incident surface and a refractivelight emergent surface. The optical system satisfies the followingconditional expressions:

ΔθgF1>0.0272,

ΔθgF2<−0.0278, and

f1×f2<0,

where ΔθgF1 and ΔθgF2 denote anomalous partial dispersion values of thefirst optical element and the second optical element for the Fraunhoferg-line and F-line, respectively, and f1 and f2 denote focal lengths ofthe first optical element and the second optical element, respectively,when the light incident surfaces and the light emergent surfaces of thefirst optical element and the second optical element are in contact withair.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional view of an optical system according to afirst numerical embodiment of the present invention.

FIG. 2A is an aberration diagram according to the first numericalembodiment.

FIG. 2B is an aberration diagram according to the first numericalembodiment.

FIG. 2C is an aberration diagram according to the first numericalembodiment.

FIG. 3 is a cross-sectional view of an optical system according to asecond numerical embodiment of the present invention.

FIG. 4 is an aberration diagram according to the second numericalembodiment.

FIG. 5 is a cross-sectional view of an optical system according to athird numerical embodiment of the present invention.

FIG. 6 is an aberration diagram according to the third numericalembodiment.

FIG. 7 is a cross-sectional view of an optical system according to afourth numerical embodiment of the present invention.

FIG. 8 is an aberration diagram according to the fourth numericalembodiment.

FIG. 9 is a cross-sectional view of an optical system according to afifth numerical embodiment of the present invention.

FIG. 10 is an aberration diagram according to the fifth numericalembodiment.

FIG. 11 is a cross-sectional view of an optical system according to asixth numerical embodiment of the present invention.

FIG. 12 is an aberration diagram according to the sixth numericalembodiment.

FIG. 13 is a cross-sectional view of an optical system according to aseventh numerical embodiment of the present invention.

FIG. 14 is an aberration diagram according to the seventh numericalembodiment.

FIG. 15 is a cross-sectional view of an optical system according to aneighth numerical embodiment of the present invention.

FIG. 16 is an aberration diagram according to the eighth numericalembodiment.

FIG. 17 is a cross-sectional view of an optical system according to aninth numerical embodiment of the present invention.

FIG. 18 is an aberration diagram according to the ninth numericalembodiment.

FIG. 19 is a cross-sectional view of an optical system according to atenth numerical embodiment of the present invention.

FIG. 20 is an aberration diagram according to the tenth numericalembodiment.

FIG. 21 is a cross-sectional view of an optical system according to aneleventh numerical embodiment of the present invention.

FIG. 22 is an aberration diagram according to the eleventh numericalembodiment.

FIG. 23 is a cross-sectional view of an optical system according to atwelfth numerical embodiment of the present invention.

FIG. 24 is an aberration diagram according to the twelfth numericalembodiment.

FIG. 25 is a cross-sectional view of an optical system according to athirteenth numerical embodiment of the present invention.

FIG. 26 is an aberration diagram according to the thirteenth numericalembodiment.

FIG. 27 is a schematic illustration of a paraxial refractive powerarrangement of the optical system according to an embodiment of thepresent invention.

FIG. 28 is a cross-sectional view of an optical system according to afourteenth numerical embodiment of the present invention.

FIG. 29 is an aberration diagram according to the fourteenth numericalembodiment.

FIG. 30 is a cross-sectional view of an optical system according to afifteenth numerical embodiment of the present invention.

FIG. 31 is an aberration diagram according to the fifteenth numericalembodiment.

FIG. 32 is a cross-sectional view of an optical system according to asixteenth numerical embodiment of the present invention.

FIG. 33 is an aberration diagram according to the sixteenth numericalembodiment.

FIG. 34 is a cross-sectional view of an optical system according to aseventeenth numerical embodiment of the present invention.

FIG. 35 is an aberration diagram according to the seventeenth numericalembodiment.

FIG. 36 is a cross-sectional view of an optical system according to aneighteenth numerical embodiment of the present invention.

FIG. 37 is an aberration diagram according to the eighteenth numericalembodiment.

FIG. 38 is a schematic illustration of a paraxial refractive powerarrangement of the optical system according to an embodiment of thepresent invention.

FIG. 39 is a diagram illustrating a wavelength characteristic of anaberration coefficient according to the present invention.

FIG. 40 is a schematic illustration of an image pickup apparatusaccording to an exemplary embodiment of the present invention.

FIG. 41 illustrates an index of refraction-wavelength characteristic ofa widely used optical element.

DESCRIPTION OF THE EMBODIMENTS

Zoom lenses and image pickup apparatuses including the zoom lensesaccording to exemplary embodiments of the present invention aredescribed below with reference to the accompanying drawings.

First Exemplary Embodiment

According to a first exemplary embodiment, an optical system includes arefractive optical element (hereinafter also referred to as an “opticalelement”) obtained by providing a refractive function to a solidmaterial that satisfies the following conditions.

As used herein, the term “solid material” of the refractive opticalelement refers to a material that is solid in a use environment of theoptical system. Accordingly, the material may be in any state before theoptical system is in use (e.g., during a fabrication period). Forexample, even when the material is liquid during a fabrication period,the material is referred to as a “solid material” if the liquid materialis cured into a solid material.

The features of an optical system OL according to the present embodimentis as follows.

A paraxial marginal ray is a paraxial ray that, when the focal length ofthe entire optical system is normalized to “1”, travels parallel to thelight axis of the optical system at a height of “1” from the light axisand is made incident on the optical system. Hereinafter, it is assumedthat an object is disposed on the left side of the optical system, and alight ray made incident on the optical system from the object sidetravels from the left to the right. A paraxial chief ray is a paraxialray that, when the focal length of the entire optical system isnormalized to “1”, passes through an intersection between the entrancepupil and the light axis of the optical system among light rays madeincident on the optical system at an angle of −45° with respect to thelight axis. The incident angle of a ray is positive if the ray ismeasured from the light axis in a clockwise direction, while theincident angle is negative if the ray is measured from the light axis ina counterclockwise direction. The intersecting point of a light axis Laand a paraxial chief ray R is defined as “P”.

The optical system OL includes a first optical element GNL1 and a secondoptical element GL1 on at least one of the enlargement side and thereduction side relative to the point P. Each of the first opticalelement GNL1 and the second optical element GNL2 has a refractive lightincident surface and a refractive light emergent surface and is made ofa solid material. Let ΔθgF1 and ΔθgF2 denote the anomalous partialdispersion values of the first optical element GNL1 and the secondoptical element GL1 for the Fraunhofer g-line and F-line, respectively.

Let f1 and f2 denote the focal lengths of the first optical element GNL1and the second optical element GL1 when the light incident surfaces andthe light emergent surfaces of the first optical element GNL1 and thesecond optical element GL1 are in contact with air.

Let Δθgd1 and Δθgd2 denote the anomalous partial dispersion values ofthe first optical element GNL1 and the second optical element GL1 forthe Fraunhofer g-line and d-line, respectively.

Let νd1 and νd2 denote the Abbe numbers of the solid materials of thefirst optical element GNL1 and the second optical element GL1,respectively.

Then, at least one of the following conditions is satisfied:

ΔθgF1>0.0272  (1)

ΔθgF2<−0.0278  (2)

Δθgd1>0.038  (3)

Δθgd2<−0.037  (4)

νd1<60  (5)

νd2<60  (6)

f1×f2<0  (7)

For the solid material of the optical element used in the optical systemaccording to the present embodiment, the Abbe number νd, the relativepartial dispersion θgd for the Fraunhofer g-line and d-line, and therelative partial dispersion θgF for the Fraunhofer g-line and F-line aredefined as follows:

νd=(Nd−1)/(NF−NC)

θgd=(Ng−Nd)/(NF−NC)

θgF=(Ng−NF)/(NF−NC)

where Ng, NF, Nd, and NC denote the indices of refraction of the solidmaterial for the Fraunhofer g-line (wavelength=435.8 nm), the FraunhoferF-line (wavelength=486.1 nm), the Fraunhofer d-line (wavelength=587.6nm), and the Fraunhofer C-line (wavelength=656.3 nm), respectively.

In general, the relative partial dispersions θgd and θgF of the solidmaterial used for a lens unit are approximated as follows:

θgd=−1.687×10⁻⁷ νd ³+5.702×10⁻⁵ νd ²−6.603×10⁻³ νd+1.462

θgF=−1.665×10⁻⁷ νd ³+5.213×10⁻⁵ νd ²−5.656×10⁻³ νd+0.7278

Here, the anomalous partial dispersion values Δθgd and ΔθgF areexpressed as follows:

Δθgd=θgd−(−1.687×10⁻⁷ νd ³+5.702×10⁻⁵ νd ²−6.603×10⁻³ νd+1.462)

ΔθgF=θgF−(−1.665×10⁻⁷ νd ³+5.213×10⁻⁵ νd ²−5.656×10⁻³ νd+0.7278)

According to the present embodiment, the optical system OL includesrefractive optical elements having refractive powers. That is, theoptical system OL includes at least one first optical element GNL1 thatis composed of a solid material having high dispersion and high relativepartial dispersion and at least one second optical element GL1 that iscomposed of a solid material having high dispersion and low relativepartial dispersion.

As used herein, the term “refractive optical element” refers to anoptical element, such as a refractive lens, that produces refractivepower using a refracting effect. Thus, a diffractive optical elementthat produces refractive power using a diffracting effect is notincluded in the category of the term “refractive optical element”.

By employing at least one first optical element GNL1 composed of a solidmaterial that satisfies conditional expression (1) and at least onesecond optical element GL1 composed of a solid material that satisfiesconditional expression (2), chromatic aberration of the optical systemin the entire range of the wavelength of visible light can besufficiently corrected.

By satisfying conditional expressions (3) and (4), chromatic aberrationof the optical system in the range of a short wavelength to a mediumwavelength can easily and sufficiently be corrected. In this way,chromatic aberration can be further sufficiently corrected in a widewavelength range from a short wavelength to a long wavelength.

By employing solid materials that satisfy conditional expressions (5)and (6), chromatic aberration of the optical system can easily becorrected.

By configuring the first optical element GNL1 and the second opticalelement GL1 so that conditional expression (7) is satisfied, chromaticaberration of the optical system in a wide wavelength range cansufficiently be corrected.

According to the present embodiment, when the first optical element GNL1and the second optical element GL1 are provided in the optical system,both optical elements can be disposed in the same lens group. At thattime, the first optical element GNL1 and the second optical element GL1may be cemented.

In addition, at least one of the surfaces of the first optical elementGNL1 and the second optical element GL1 can be aspherical in order tocorrect the aberrations.

Furthermore, at least one of the surfaces of the first optical elementGNL1 and the second optical element GL1 can be in contact with air inorder to correct the aberrations.

Examples of the solid material (hereinafter also referred to as an“optical material”) that satisfies conditional expression (1) include avariety of resins. Among the variety of resins, a UV-curable resin(Nd=1.63, νd=22.7, and θgF=0.69) and N-polyvinyl carbazole (Nd=1.696,νd=17.7, and θgF=0.69) are typical optical materials that satisfyconditional expression (1). However, in addition to these materials, anysolid material that satisfies conditional expression (1) can beemployed.

In addition, an optical material having a characteristic that isdifferent from that of a widely used glass material can be used.Examples of such an optical material include a mixture of a syntheticresin and inorganic oxide nanoparticles dispersed therein. Examples ofthe inorganic oxide nanoparticles include TiO₂ particles (Nd=2.304 andνd=13.8), Nb₂O₅ particles (Nd=2.367 and νd=14.0), ITO particles(Nd=1.8571 and νd=5.69), CrO₃ particles (Nd=2.2178 and νd=13.4), andBaTiO₃ particles (Nd=2.4362 and νd=11.3).

Among these types of inorganic oxide, by dispersing TiO₂ particles(Nd=2.304, νd=13.8, and θgF=0.87) in a synthetic resin in an appropriatevolume ratio, an optical material that satisfies conditional expression(1) can be obtained. In addition, by dispersing ITO particles(Nd=1.8571, νd=5.69, and θgF=0.873) in a synthetic resin in anappropriate volume ratio, an optical material that satisfies conditionalexpression (2) can be obtained. However, any solid material thatsatisfies conditional expression (2) can be employed.

According to the present embodiment, by using an optical material havinga relative partial dispersion higher than that of a widely used opticalmaterial and an optical material having a relative partial dispersionlower than that of a widely used optical material, the chromaticaberration is sufficiently corrected.

In the wavelength-dependent characteristic of the index of refraction(dispersion characteristic) of an optical material, the Abbe numberrepresents the slope of the dispersion characteristic curve, and therelative partial dispersion represents the curvature of the dispersioncharacteristic curve.

In general, the index of refraction of an optical material in ashort-wavelength range is higher than that in a long-wavelength range.At that time, the Abbe number and the relative partial dispersion arepositive. Accordingly, the dispersion characteristic curve is downwardlyconvex. A change in the index of refraction with respect to a change inthe wavelength increases towards a short-wavelength range. For example,refractive index characteristics with respect to a wavelength for S-BSL7(Nd=1.516 and νd=64.1) and S-TIH53 (Nd=1.847 and νd=23.8) available fromOHARA corporation are shown in FIG. 41.

In addition, a high-dispersion optical material having a smaller Abbenumber tends to have a higher relative partial dispersion. In widelyused optical materials, the relative partial dispersion substantiallylinearly changes with respect to the Abbe number. However, an opticalmaterial having an anomalous partial dispersion changes differently fromthe linear change. A typical example of such an anomalous partialdispersion material is fluorite.

The wavelength-dependent characteristic curve of a chromatic aberrationcoefficient of an optical material having a high relative partialdispersion has a large curvature in a short-wavelength range, comparedwith that of a widely used optical material.

When the refractive power of the lens surface of an optical materialhaving a high relative partial dispersion is changed in order to controlthe chromatic aberration, the slope of the entire wavelength-dependentcharacteristic curve of a chromatic aberration coefficient changes suchthat the entire wavelength-dependent characteristic curve rotates abouta point of a reference design wavelength. In particular, the change issignificant in a short-wavelength range for an optical material having ahigh relative partial dispersion. As a result, the slope of the entirewavelength-dependent characteristic curve is changed while significantlychanging the curvature in the short-wavelength range.

By using this property, the curvature of the wavelength-dependentcharacteristic curve of a chromatic aberration coefficient in theshort-wavelength range can be canceled. However, it is difficult tocorrect the remaining slope of the wavelength-dependent characteristiccurve of a chromatic aberration coefficient at the same time. Inaddition, the correction of the curvature in the short-wavelength rangerelatively increases chromatic aberration in a long-wavelength range. Toprevent the increase in chromatic aberration in a long-wavelength range,the refractive power of an appropriate one of the glass surfaces of theoptical system needs to be changed. However, this is not suitable forcorrecting a variety of aberrations other than chromatic aberration.

In contrast, the wavelength-dependent characteristic curve of achromatic aberration coefficient of an optical material having a lowrelative partial dispersion has a small curvature in a short-wavelengthrange. Accordingly, the chromatic aberration coefficient linearlychanges with a change in wavelength, compared with that of a widely usedoptical material. When the refractive power of the lens surface of anoptical material having a low relative partial dispersion is changed inorder to control the chromatic aberration, the slope of the entirewavelength-dependent characteristic curve of a chromatic aberrationcoefficient changes such that the entire wavelength-dependentcharacteristic curve rotates about a point of a reference designwavelength while relatively retaining linearity with respect to thewavelength. In this way, the slope of the wavelength-dependentcharacteristic curve of a chromatic aberration coefficient can becorrected.

Accordingly, by employing an optical material having a low relativepartial dispersion in addition to an optical material having a highrelative partial dispersion, the curvature of the wavelength-dependentcharacteristic curve of a chromatic aberration coefficient in ashort-wavelength range and the slope of the entire wavelength-dependentcharacteristic curve can be corrected at the same time. That is, thechromatic aberration of the optical system can be sufficiently correctedin a wide wavelength range of the g-line to C-line.

Such correction of chromatic aberration of an optical system isdescribed next with reference to an optical system including arefractive optical system portion GNL using an optical material having ahigh relative partial dispersion, a refractive optical system portion GLusing an optical material having a low relative partial dispersion, anda refractive optical system portion G using a widely used opticalmaterial having a normal relative partial dispersion.

Chromatic aberration of the refractive optical system portion G iscorrected to some extent first. Then, a relatively high-dispersionoptical material is selected for a negative lens included in therefractive optical system portion G. The slope of the entirewavelength-dependent characteristic curve of a chromatic aberrationcoefficient of the refractive optical system portion G is changed whilethe portion in a short-wavelength range is significantly curved from theoriginal shape.

At that time, an appropriate refractive power is provided to therefractive optical system portion GNL, and a relatively high-dispersionoptical material is selected for a positive lens included in therefractive optical system portion G. However, in the case where therefractive optical system portion GNL is composed of a widely usedoptical material having a relative partial dispersion that is uniformfor an Abbe number, the refractive optical system portion GNL ispartially responsible equally for a curvature component and a slopecomponent of the wavelength-dependent characteristic curve of achromatic aberration coefficient of the refractive optical systemportion G. Therefore, the curvature component and the slope componentcannot be canceled at the same time. As a result, it is difficult tocorrect the chromatic aberration sufficiently.

In contrast, in the case where the refractive optical system portion GNLis composed of an optical material having a relative partial dispersionhigher than that of a widely used optical material, the refractiveoptical system portion GNL is relatively largely responsible for theslope component of the entire wavelength-dependent characteristic curveof a chromatic aberration coefficient of the main refractive opticalsystem portion G. Therefore, the curvature component can be mainlycanceled. As a result, the slope of the entire wavelength-dependentcharacteristic curve of a chromatic aberration coefficient can bechanged while increasing linearity from the original shape.

At that time, by further providing the refractive optical system portionGL with an appropriate refractive power of a sign opposite to that ofthe refractive optical system portion GNL, the slope of the entirewavelength-dependent characteristic curve of a chromatic aberrationcoefficient of the refractive optical system portion G can be corrected.However, if the refractive optical system portion GL is composed of awidely used optical material, the refractive optical system portion GLhas a characteristic in which the wavelength-dependent characteristiccurve of a chromatic aberration coefficient is relatively largely convexin a direction opposite to that corresponding to thewavelength-dependent characteristic curve of the refractive opticalsystem portion G. Accordingly, although the slope component of theentire wavelength-dependent characteristic curve of a chromaticaberration coefficient can be canceled, a curvature component thatincreases the chromatic aberration occurs.

In contrast, in the case where the refractive optical system portion GLis composed of an optical material having a low relative partialdispersion, the linearity of the wavelength-dependent characteristiccurve of a chromatic aberration coefficient of the refractive opticalsystem portion GL is relatively increased. That is, by changing therefractive power of the refractive optical system portion GL in order tocorrect the chromatic aberration, the slope of the wavelength-dependentcharacteristic curve of a chromatic aberration coefficient can bechanged so that the wavelength-dependent characteristic curve rotatesabout the point of the design reference wavelength while substantiallymaintaining linearity.

As described above, by using the refractive optical system portion GNL,the refractive optical system portion GL, and the refractive opticalsystem portion G, the slope component and the curvature component of thewavelength-dependent characteristic curve of a chromatic aberrationcoefficient can be relatively easily corrected at the same time.

To sufficiently correct chromatic aberration by using one of therefractive optical system portion GNL and the refractive optical systemportion GL, the refractive power of a lens surface of one of therefractive optical system portions GNL and GL and the refractive powerof a lens surface of the refractive optical system portion G need to beincreased.

That is, by employing the refractive optical system portions GNL and GL,the refractive power of each of the refractive optical system portionGNL and the refractive optical system portion GL can be relativelyreduced. As a result, the thickness of the solid material in the lightaxis direction can be reduced. Furthermore, by employing the refractiveoptical system portions GNL and GL, the chromatic aberration can bereduced without significantly changing the refractive power of therefractive optical system portion G. Accordingly, a variety ofaberrations other than the chromatic aberration can be maintainedunchanged.

At that time, in order to independently correct chromatic aberration, itis desirable that the refractive optical system portion GNL and therefractive optical system portion GL is composed of an optical materialhaving a small Abbe number, that is, a high-dispersion optical material.Furthermore, it is desirable that at least one refractive optical systemportion GNL and at least one refractive optical system portion GL aredisposed on the enlargement side or the reduction side relative to thepoint P at which the paraxial chief ray intersects the light axis. Thisis described in detail next with reference to an axial chromaticaberration coefficient and a chromatic aberration coefficient ofmagnification of a lens surface.

Let ΔΨ denote a change in refractive power of a surface of a refractivelens, and ν denote the Abbe number. Let h and H denote the heights ofthe paraxial marginal ray and the paraxial chief ray from the light axiswhen the paraxial marginal ray and the paraxial chief ray pass throughthe surface of the refractive lens, respectively. Then, a change ΔL inthe axial chromatic aberration coefficient and a change ΔT in achromatic aberration coefficient of magnification can be expressed asfollows:

ΔL=h ²·ΔΨ/ν  (a)

ΔT=h·H·ΔΨ/ν  (b)

As can be seen from equations (a) and (b), the changes in theseaberration coefficients with respect to a change in the refractive powerof the lens surface increase as the absolute value of the Abbe numberdecreases (i.e., as the dispersion increases). Accordingly, by using ahigh-dispersion material having a small absolute value of the Abbenumber, the change amount of the refractive power that is required forobtaining a desired chromatic aberration can be reduced.

According to an aberration theory, this allows the chromatic aberrationto be controlled without significantly affecting the sphericalaberration, coma aberration, and astigmatism aberration. Thus, thechromatic aberration can be highly independently controlled.

However, if a low-dispersion material is employed, the change amount ofthe refractive power that is required for obtaining a desired chromaticaberration is increased. With the increase in the change amount of therefractive power, a variety of aberrations, such as sphericalaberration, significantly change. Thus, the chromatic aberration cannotbe independently controlled. Therefore, in order to correct aberrations,it can be useful that, among the lenses of the optical system, at leastone of the surfaces of the lenses is a surface of a refractive lens madeof a high-dispersion material.

In addition, equations (a) and (b) indicate that the changes in theaxial chromatic aberration coefficient and the chromatic aberrationcoefficient of magnification are determined by the values of the heightsh and H. Using this result, the optimal arrangement of the refractiveoptical system portion GNL and the refractive optical system portion GLin the optical system is described next.

To sufficiently correct chromatic aberration, the slope component andthe curvature components need to be corrected at the same time. However,if the refractive power change ΔΨ is decreased, sufficient correction ofthe chromatic aberration cannot be achieved. In contrast, if therefractive power change ΔΨ is increased, the thickness of an opticalelement serving as a lens is increased.

In general, since the transmittance of the optical material of therefractive optical system portion GNL and the refractive optical systemportion GL having an anomalous partial dispersion characteristic is low,the thickness of a lens composed of the optical material needs to berelatively reduced when the refractive optical system portions are usedfor lenses.

That is, in order to reduce the thicknesses of the refractive opticalsystem portion GNL and the refractive optical system portion GL andsufficiently correct the chromatic aberration, the effects of thearrangement on the slope component and the curvature component of thewavelength-dependent characteristic curve of a chromatic aberrationcoefficient can be substantially the same. Accordingly, the heights hand H from the light axis in the refractive optical system portion GNLand the refractive optical system portion GL can be similar values.

The plus/minus sign of H on the enlargement side is different from thaton the reduction side. That is, when the refractive optical systemportion GNL is disposed on the enlargement side of the point P and therefractive optical system portion GL is disposed on the reduction sideof the point P, the values of h and H are significantly different.Therefore, in order to correct chromatic aberration, at least onerefractive optical system portion GNL and at least one refractiveoptical system portion GL can be disposed on the enlargement side of thepoint P or on the reduction side of the point P. At that time, to cancelthe curvature component and the slope component of thewavelength-dependent characteristic curve of a chromatic aberrationcoefficient, the product of the focal length (f1) of the refractiveoptical system portion GNL and the focal length (f2) of the refractiveoptical system portion GL can be negative, as indicated by conditionalexpression (7).

The telephoto optical system is configured so that the maximum height ofthe paraxial marginal ray from the light axis when the paraxial marginalray passes through the lens surface on the enlargement side of the pointP where the light axis intersects the paraxial chief ray is greater thanthat on the reduction side of the point P. In the telephoto opticalsystem, by disposing the refractive optical system portion GNL and therefractive optical system portion GL on the enlargement side, the axialchromatic aberration and the chromatic aberration of magnification canbe sufficiently corrected.

In contrast, the retrofocus optical system is configured so that themaximum height of the paraxial marginal ray from the light axis when theparaxial marginal ray passes through the lens surface on the enlargementside of the point P where the light axis intersects the paraxial chiefray is less than that on the reduction side of the point P. In theretrofocus optical system, by disposing the refractive optical systemportion GNL and the refractive optical system portion GL on thereduction side, the axial chromatic aberration and the chromaticaberration of magnification can be sufficiently corrected.

If the refractive optical system portion GNL and the refractive opticalsystem portion GL are disposed so that the distance therebetween isrelatively large, the heights h and H at the lens surfaces thereof aresignificantly different. At that time, the aberration coefficients ΔLand ΔT of the lens surfaces thereof are significantly different.Accordingly, the slope component and the curvature component of thewavelength-dependent characteristic curve of a chromatic aberrationcoefficient of the entire optical system are significantly differentlyaffected.

However, if the refractive optical system portion GNL and the refractiveoptical system portion GL are disposed near each other, the heights hand H at the lens surfaces thereof are relatively similar values. Atthat time, the slope component and the curvature component of thewavelength-dependent characteristic curve of a chromatic aberrationcoefficient of the entire optical system are substantially equallyeffected. Thus, the chromatic aberration can be sufficiently corrected.

As a result, it is desirable that the refractive optical system portionGNL and the refractive optical system portion GL are disposed near eachother. For example, the refractive optical system portion GNL and therefractive optical system portion GL can be cemented. In addition, sinceboth the heights h and H do not significantly change in the same lensgroup of the optical system, it is more desirable that the refractiveoptical system portions GNL and GL are disposed in the same lens group.

In general, when a lens group is moved in order to perform zooming andfocusing and control the position of the image, the states of a ray madeincident on the lens groups change, and therefore, aberrations occurringin the lens groups change. Accordingly, in order to sufficiently correctthe aberrations of the optical system in all the use cases, aberrationcoefficients that simultaneously change in all the use cases need to bedetermined for each of the lens groups. By disposing the refractiveoptical system portions GNL and GL in the same lens group, desiredaberration values can be easily obtained.

In addition, if the thicknesses of the refractive optical systemportions GNL and GL are reduced, a change in the thickness due to thesurrounding environment is reduced. Furthermore, by satisfyingconditional expression (7), the resistance to the surroundingenvironment can be increased.

A variety of aberrations including chromatic aberration are corrected bythe refractive optical system portions GNL and GL in cooperation with awidely used optical material. Accordingly, the characteristics of therelative partial dispersions of the refractive optical system portionsGNL and GL need to be different from that of the widely used opticalmaterial in order to correct the aberrations. However, a stronganomalous partial dispersion should be avoided.

When a lens made of an optical material having a characteristicsignificantly different from that of a widely used optical material isemployed, the curvature of the wavelength-dependent characteristic curveof a chromatic aberration coefficient of the lens surface isparticularly large. To correct the large curvature component, therefractive powers of other lenses need to be increased. This gives asignificant impact on the spherical aberration, the coma aberration, andthe astigmatism aberration. Thus, it is difficult to correct theseaberrations.

That is, the material of the refractive optical system portion GNL needsto be an optical material having a relative partial dispersion higherthan that of a widely used optical material, but not having a relativepartial dispersion significantly different from that of a widely usedoptical material.

To obtain further sufficient correction of chromatic aberration, therange of the anomalous partial dispersion value ΔθgF1 defined inconditional expression (1) can be redefined as follows:

0.0272<ΔθgF1 <0.2832  (1a)

To obtain still further sufficient correction of chromatic aberration,the range of the anomalous partial dispersion value ΔθgF1 defined inconditional expression (1a) can be redefined as follows:

0.0342<ΔθgF1 <0.2832  (1b)

To obtain further sufficient correction of chromatic aberration, therange of the anomalous partial dispersion value ΔθgF2 defined inconditional expression (2) can be redefined as follows:

−0.4278<ΔθgF2<−0.0528  (2a)

To obtain still further sufficient correction of chromatic aberration,the range of the anomalous partial dispersion value ΔθgF2 defined inconditional expression (2a) can be redefined as follows:

−0.4278<ΔθgF2<−0.0778  (2b)

To obtain further sufficient correction of chromatic aberration, therange of the anomalous partial dispersion value Δθgd1 defined inconditional expression (3) can be redefined as follows:

0.038<Δθgd1<0.347  (3a)

To obtain still further sufficient correction of chromatic aberration,the range of the anomalous partial dispersion value Δθgd1 defined inconditional expression (3a) can be redefined as follows:

0.051<Δθgd1<0.347  (3b)

To obtain further sufficient correction of chromatic aberration, therange of the anomalous partial dispersion value Δθgd2 defined inconditional expression (4) can be redefined as follows:

−0.5620<Δθgd2<−0.062  (4a)

To obtain still further sufficient correction of chromatic aberration,the range of the anomalous partial dispersion value Δθgd1 defined inconditional expression (4a) can be redefined as follows:

−0.5620<Δθgd2<−0.112  (4b)

To obtain further sufficient correction of chromatic aberration, theranges of the Abbe numbers νd1 and νd2 defined in conditionalexpressions (5) and (6) can be redefined as follows:

νd1<50  (5a)

νd2<50  (6a)

To obtain still further sufficient correction of chromatic aberration,the ranges of the Abbe numbers νd1 and νd2 defined in conditionalexpressions (5a) and (6a) can be redefined as follows:

νd1<45  (5b)

νd2<45  (6b)

To obtain yet still further sufficient correction of chromaticaberration, the ranges of the Abbe numbers νd1 and νd2 defined inconditional expressions (5b) and (6b) can be redefined as follows:

νd1<40  (5c)

νd2<40  (6c)

In the above-described exemplary embodiments, the first optical elementGNL1 and the second optical element GL1 made of an optical material thatsatisfies conditional expressions (1) and (2) are employed for a lensand refractive layers provided on a lens of the optical system. Inaddition, if the refractive surface composed of such an optical materialis aspherical, chromatic aberration flare, such as spherical aberrationof a color, can be corrected. Furthermore, by forming an interfacebetween the optical element and air atmosphere or between the opticalelement and an optical material having a relatively low index ofrefraction, the chromatic aberration can be relatively significantlychanged by slightly changing the radius of curvature of the interface.

Exemplary embodiments in which an optical element composed of theoptical material that satisfies conditional expressions (1) to (7) isemployed for a particular optical system are described in detail next.In these exemplary embodiments, a UV-curable resin 1, N-polyvinylcarbazole, or a mixture of a UV-curable resin 2 and TiO₂ fine particlesdispersed therein is used for an optical material that satisfiesconditional expressions (1), (3), and (5). A mixture of the UV-curableresin 2 and ITO fine particles dispersed therein or a mixture ofN-polyvinyl carbazole and ITO fine particles dispersed therein is usedfor an optical material that satisfies conditional expressions (2), (4),and (6).

An optical system used in each of the exemplary embodiments is aphoto-taking lens system used in an image pickup apparatus, such as avideo camera, a digital camera, or a silver-halide film camera. In thecross-sectional views of lenses, an object is located on the left side(the front side), and an image plane is located on the right side (therear side).

In the case where the optical systems of the exemplary embodiments areused for projection lenses of, for example, projectors, a screen islocated on the left side, and an image to be projected is located on theright side.

In the cross-sectional views of lenses, “i” represents the order of alens group numbered from the object. “L1” represents an ith lens group.

In addition, “SP” represents an aperture stop. “G” represents an opticalblock including an optical filter, a face plate, a quartz low-passfilter, and an infrared-cut filter.

Furthermore, an image plane IP is shown in the drawings. When theoptical system is used for a photo-taking lens of a video camera or adigital still camera, an imaging surface of a solid-state image pickupelement (a photoelectric conversion element), such as a charged coupleddevice (CCD) sensor or a complementary metal oxide semiconductor (CMOS)sensor, is disposed in the image plane IP. When the optical system isused for a photo-taking lens of a silver-halide film camera, alight-sensitive surface corresponding to the film surface is disposed inthe image plane IP.

In aberration diagrams, “d” and “g” represent the d-line and g-line,respectively. “ΔM” and “ΔS” represent the meridional image plane and thesagittal image plane, respectively. The chromatic aberration ofmagnification is represented using the g-line. “ω” denotes the halfangle of field. “Fno” denotes the F number.

According to the first exemplary embodiment, as shown in FIG. 1, anoptical system is a zoom lens having a zoom ratio of about 12 andincluding four lens groups. That is, the optical system includes a firstlens group L1 having a positive refractive power, a second lens group L2having a negative refractive power, a third lens group L3 having apositive refractive power, and a fourth lens group L4 having a positiverefractive power in this order from an object side to an image side.

When zooming is performed from the wide-angle end to the telephoto end,the lens groups are moved in trajectories as indicated by arrows. Thatis, when zooming is performed, the lens groups are moved so that thedistances between the lens groups are changed.

In the present embodiment, the optical system includes a lens composedof a mixture of a UV-curable resin and ITO fine particles dispersedtherein. In FIG. 1, the first optical element GNL1 is a lens (layer)composed of the UV-curable resin 1. The second optical element GL1 is alens (layer) composed of a mixture of the UV-curable resin 2 and 14.2%by volume ITO fine particles dispersed therein.

According to the first exemplary embodiment, the lens GNL1 composed ofthe UV-curable resin 1 and the lens GL1 composed of a mixture of theUV-curable resin 2 and ITO fine particles are used in the first lensgroup L1. The first lens group L1 is located on the object side amongthe lens groups included in the zoom lens. When the paraxial marginalray passes through the first lens group L1, the height of the paraxialmarginal ray from the light axis is relatively large. In addition, thelens GNL1 and the lens GL1 are in tight contact with each other and arecemented between the other lenses.

The lens (layer) GNL1 composed of the UV-curable resin 1 has a positiverefractive power. The lens (layer) GL1 composed of a mixture includingthe ITO fine particles has a negative refractive power. In this way,when zooming is performed from the wide-angle end to the telephoto end,axial chromatic aberration and chromatic aberration of magnification aresufficiently corrected. In addition, the size of the entire opticalsystem can be reduced.

According to second to sixth exemplary embodiments, as shown in FIGS. 3,5, 7, 9, and 11, optical systems are telephoto lenses. As used herein,the term “telephoto lens” refers to a lens system having a total lenslength that is shorter than the focal length thereof.

According to a second exemplary embodiment, as shown in FIG. 3, theoptical system is an ultra-telephoto lens having a focal length of 300mm. The optical system includes a first lens group L1 having a positiverefractive power, a second lens group L2 having a negative refractivepower, and a third lens group L3 having a positive refractive power. Thesecond lens group L2 is moved along the light axis for a focusingpurpose.

According to the exemplary present embodiment, the lens (layer) GNL1composed of the UV-curable resin 1 is employed as part of the opticalsystem. In addition, the lens (layer) GL1 composed of a mixture of theUV-curable resin 2 and 14.2% by volume ITO fine particles dispersedtherein is employed.

That is, according to the exemplary present embodiment, the opticalsystem includes the lens (layer) GNL1 composed of the UV-curable resin 1and having a positive refractive power and the lens (layer) GL1 composedof a mixture of the UV-curable resin 2 and ITO fine particles and havinga negative refractive power on the object side where a point at whichthe paraxial marginal ray passes the lenses has a relatively largeheight from the light axis. In addition, the lens GNL1 is in tightcontact with the lens GL1 so that the contact surface is aspherical. Inthis way, axial chromatic aberration and chromatic aberration ofmagnification are sufficiently corrected. Thus, a compactultra-telephoto lens having a telephoto ratio of 0.681 can be achieved.

According to a third exemplary embodiment, as shown in FIG. 5, theoptical system is an ultra-telephoto lens having a focal length of 300mm. The optical system includes a first lens group L1 having a positiverefractive power, a second lens group L2 having a negative refractivepower, and a third lens group L3 having a positive refractive power. Thesecond lens group L2 is moved along the light axis for a focusingpurpose.

According to the present exemplary embodiment, the lens (layer) GNL1composed of a mixture of the UV-curable resin 2 and 20% by volume TiO₂fine particles dispersed therein is employed as part of the opticalsystem. In addition, the lens (layer) GL1 composed of a mixture of theUV-curable resin 2 and 20% by volume ITO fine particles dispersedtherein is employed.

According to the third exemplary embodiment, the optical system includesthe lens (layer) GNL1 composed of a mixture of the UV-curable resin 2and TiO₂ fine particles dispersed therein and having a positiverefractive power and the lens (layer) GL1 composed of a mixture of theUV-curable resin 2 and ITO fine particles and having a negativerefractive power on the object side where a point at which the paraxialmarginal ray passes the lenses has a relatively large height from thelight axis. In this way, axial chromatic aberration and chromaticaberration of magnification are sufficiently corrected. Thus, a compactultra-telephoto lens having a telephoto ratio of 0.680 can be achieved.

According to a fourth exemplary embodiment, as shown in FIG. 7, theoptical system is an ultra-telephoto lens having a focal length of 300mm. The optical system includes a first lens group L1 having a positiverefractive power, a second lens group L2 having a negative refractivepower, and a third lens group L3 having a positive refractive power. Thesecond lens group L2 is moved along the light axis for a focusingpurpose.

According to the present exemplary embodiment, the lens (layer) GNL1composed of N-polyvinyl carbazole is employed as part of the opticalsystem. In addition, the lens (layer) GL1 composed of a mixture of theUV-curable resin 2 and 5% by volume ITO fine particles dispersed thereinis employed.

According to the fourth exemplary embodiment, the optical systemincludes the lens (layer) GNL1 composed of a mixture of the UV-curableresin 2 and TiO₂ fine particles dispersed therein and having a positiverefractive power and the lens (layer) GL1 composed of a mixture of theUV-curable resin 2 and ITO fine particles and having a negativerefractive power on the object side where a point at which the paraxialmarginal ray passes the lenses has a relatively large height from thelight axis. In this way, axial chromatic aberration and chromaticaberration of magnification are sufficiently corrected. Thus, a compactultra-telephoto lens having a telephoto ratio of 0.731 can be achieved.

According to a fifth exemplary embodiment, as shown in FIG. 9, theoptical system is an ultra-telephoto lens having a focal length of 300mm. The optical system includes a first lens group L1 having a positiverefractive power, a second lens group L2 having a negative refractivepower, and a third lens group L3 having a positive refractive power. Thesecond lens group L2 is moved along the light axis direction for afocusing purpose.

According to the present exemplary embodiment, the lens (layer) GNL1composed of a mixture of the UV-curable resin 2 and 3% by volume TiO₂fine particles dispersed therein is employed as part of the opticalsystem. In addition, the lens (layer) GL1 composed of a mixture ofN-polyvinyl carbazole and 10% by volume ITO fine particles dispersedtherein is employed.

According to the fifth exemplary embodiment, the optical system includesthe lens (layer) GNL1 composed of a mixture including TiO₂ fineparticles dispersed therein and having a positive refractive power andthe lens (layer) GL1 composed of a mixture including ITO fine particlesand having a negative refractive power on the object side where a pointat which the paraxial marginal ray passes the lenses has a relativelylarge height from the light axis. In this way, axial chromaticaberration and chromatic aberration of magnification are sufficientlycorrected. Thus, a compact ultra-telephoto lens having a telephoto ratioof 0.748 can be achieved.

According to a sixth exemplary embodiment, as shown in FIG. 11, theoptical system is an ultra-telephoto lens having a focal length of 300mm. The optical system includes a first lens group L1 having a positiverefractive power, a second lens group L2 having a negative refractivepower, and a third lens group L3 having a positive refractive power. Thesecond lens group L2 is moved along the light axis for a focusingpurpose.

According to the present exemplary embodiment, the lens (layer) GNL1composed of the UV-curable resin 1 is employed as part of the opticalsystem. In addition, the lens (layer) GL1 composed of a mixture of theUV-curable resin 2 and 5% by volume ITO fine particles dispersed thereinis employed.

According to the sixth exemplary embodiment, the optical system includesthe lens (layer) GNL1 composed of an UV-curable resin and having apositive refractive power and the lens (layer) GL1 composed of a mixtureincluding ITO fine particles and having a negative refractive power onthe object side where a point at which the paraxial marginal ray passesthe lenses has a relatively large height from the light axis. In thisway, axial chromatic aberration and chromatic aberration ofmagnification are sufficiently corrected. Thus, a compactultra-telephoto lens having a telephoto ratio of 0.737 can be achieved.

According to a seventh exemplary embodiment, as shown in FIG. 13, anoptical system is a wide-angle (retrofocus) lens. As used herein, theterm “wide-angle lens” refers to a lens system having the focal lengththat is shorter than the total lens length thereof.

According to the seventh exemplary embodiment, as shown in FIG. 13, theoptical system is a wide-angle lens having a focal length of 24.5 mm.The optical system includes a first lens group L1 having a negativerefractive power, a second lens group L2 having a negative refractivepower, and a third lens group L3 having a positive refractive power. Thefirst lens group L1 is moved along the light axis for a focusingpurpose.

According to the present exemplary embodiment, the lens (layer) GNL1composed of the UV-curable resin 1 is employed as part of the opticalsystem. In addition, the lens (layer) GL1 composed of a mixture of theUV-curable resin 2 and 5% by volume ITO fine particles dispersed thereinis employed.

According to the seventh exemplary embodiment, the optical systemincludes the lens (layer) GNL1 composed of a UV-curable resin and havinga positive refractive power and the lens (layer) GL1 composed of amixture including ITO fine particles and having a negative refractivepower on the image side of the point P at which the light axisintersects the paraxial chief ray. In this way, a wide-angle lens havingsufficiently corrected axial chromatic aberration and chromaticaberration of magnification can be achieved.

Particular values used in first to seventh numerical embodiments, whichcorrespond to the first to seventh exemplary embodiments, are describedbelow. In the following numerical embodiments, i denotes the order of asurface numbered from the object. Ri denotes the radius of curvature ofthe ith optical surface, and Di denotes a distance between the ithsurface and the (i+1)th surface along the light axis. Ni and vi denotethe index of refraction and the Abbe number of a material of the ithoptical element (excluding a lens (layer) composed of a resin, amaterial including TiO₂ fine particles dispersed therein, or a materialincluding ITO fine particles dispersed therein) for the d-line,respectively. NGNLj and vGNLj denote the index of refraction and theAbbe number of a material of a lens GNLj composed of a resin, a materialincluding TiO₂ fine particles dispersed therein, or a material includingITO fine particles dispersed therein for the d-line, respectively. Here,j=1, 2, . . . “f” denotes the focal length of an optical system. “Fno”denotes the F number. “ω” denotes the half angle of field.

The shape of an aspherical surface is expressed by the followingequation:

${x(h)} = {\frac{\left( {1/r} \right)h^{2}}{1 + \sqrt{\left\{ {1 - {\left( {1 + k} \right)\left( {h/r^{2}} \right)}} \right\}}} + {B\; h^{4}} + {C\; h^{6}} + {D\; h^{8}} + {E\; h^{10}} + \ldots}$

where

X is an amount of displacement from the surface vertex in the light axisdirection,

h is a height from the light axis in a direction perpendicular to thelight axis,

r is the paraxial radius of curvature,

k is the conic constant, and

B, C, D, E, . . . are aspherical coefficients at respective orders.

In Table 3 and in each aspherical coefficient, “E±XX” means “×10^(±XX)”.

In the first numerical embodiment, the five planes (the planes having aradius of curvature of ∞) that are the closest to the image sidecorrespond to an insertion filter, an optical lowpass filter, aninfrared cut filter and the like.

Table 1 shows the indices of refraction, the Abbe numbers, and therelative partial dispersions of the refractive optical system portionsGNL1 and GL1 for d-line, g-line, C-line, and F-line. Table 2 shows theindices of refraction, the Abbe numbers, and the relative partialdispersions of the UV-curable resin 2, ITO, and TiO₂ for d-line, g-line,C-line, and F-line. Table 3 shows the focal lengths fGNLj and fGLj ofthe refractive optical elements GNLj and GLj.

(First Numerical Embodiment) f = 6.15~20.45~71.28 Fno = 2.88~3.80~3.552ω = 60.68°~19.96°~5.78° R1 = 71.850 D1 = 2.00 N1 = 1.8500 ν1 = 23.0 R2= 31.416 D2 = 0.99 NGNL1 = 1.6356 νGNL1 = 22.7 R3 = 40.451 D3 = 0.05NGL1 = 1.5648 νGL1 = 20.0 R4 = 37.918 D4 = 4.41 N2 = 1.4932 ν2 = 69.7 R5= −323.443 D5 = 0.15 R6 = 33.430 D6 = 3.10 N3 = 1.7498 ν3 = 51.4 R7 =151.878 D7 = Variable R8 = 57.767 D8 = 0.90 N4 = 1.8582 ν4 = 42.8 R9 =8.856 D9 = 3.82 R10 = −30.420 D10 = 0.75 N5 = 1.6017 ν5 = 61.3 R11 =24.070 D11 = 0.79 R12 = 16.552 D12 = 1.89 N6 = 1.9152 ν6 = 20.6 R13 =50.082 D13 = Variable R14 = ∞ (Aperture Stop) D14 = Variable R15 = 7.672(Aspherical D15 = 2.81 N7 = 1.5604 ν7 = 63.9 R16 = 262.567 Surface) D16= 2.30 R17 = 20.630 D17 = 0.70 N8 = 1.8167 ν8 = 31.9 R18 = 7.094 D18 =0.98 R19 = 36.555 D19 = 1.70 N9 = 1.6129 ν9 = 60.7 R20 = −67.789 D20 =Variable R21 = ∞ D21 = Variable R22 = 16.043 D22 = 2.65 N10 = 1.7753 ν10= 50.2 R23 = −12.932 D23 = 0.80 N11 = 1.7103 ν11 = 29.1 R24 = 116.489D24 = Variable R25 = ∞ D25 = 0.31 N12 = 1.5443 ν12 = 70.6 R26 = ∞ D26 =0.50 N13 = 1.4940 ν13 = 75.0 R27 = ∞ D27 = 0.80 R28 = ∞ D28 = 0.50 N14 =1.4983 ν14 = 65.1 R29 = ∞ Focal Length Variable Distance 6.15 20.4571.28 D7 0.80 18.23 31.76 D13 25.61 13.43 1.29 D14 9.13 1.20 2.48 D201.10 2.19 4.98 D21 3.00 4.99 5.92 D24 9.09 12.28 6.87 AsphericalCoefficient k B C D E 15th −4.1923E−01 −6.0718E−05 7.5575E−08−2.3825E−08 4.7278E−10 Surface

(Second Numerical Embodiment) f = 294.0 Fno = 4.14 2ω = 8.42° R1 = ∞ D1= 3.30 N1 = 1.5860 ν1 = 58.6 R2 = ∞ D2 = 0.15 R3 = 193.388 D3 = 8.76 N2= 1.5212 ν2 = 67.0 R4 = −173.765 D4 = 1.20 NGNL1 = 1.6356 νGNL1 = 22.7R5 = −131.984 (Aspherical D5 = 0.05 NGL1 = 1.5648 νGL1 = 20.0 R6 =−161.149 Surface) D6 = 0.15 R7 = 74.247 D7 = 6.64 N3 = 1.4870 ν3 = 70.4R8 = 176.418 D8 = 5.16 R9 = −257.193 D9 = 3.40 N4 = 1.7641 ν4 = 27.9 R10= 845.002 D10 = 0.15 R11 = 50.201 D11 = 8.33 N5 = 1.4870 ν5 = 40.4 R12 =138.171 D12 = 6.50 R13 = 45.368 D13 = 3.00 N6 = 1.8490 ν6 = 26.7 R14 =33.543 D14 = 11.75 R15 = ∞ (Aperture Stop) D15 = 0.00 R16 = ∞ D16 = 4.00R17 = 159.894 D17 = 3.17 N7 = 1.7294 ν7 = 27.0 R18 = −216.482 D18 = 2.00N8 = 1.8850 ν8 = 41.0 R19 = 81.708 D19 = 32.13 R20 = 99.214 D20 = 1.60N9 = 1.8500 ν9 = 23.0 R21 = 26.424 D21 = 7.15 N10 = 1.5812 ν10 = 39.5R22 = −50.918 D22 = 0.16 R23 = ∞ D23 = 0.00 R24 = 95.554 D24 = 4.32 N11= 1.8600 ν11 = 26.4 R25 = −37.008 D25 = 1.50 N12 = 1.7800 ν12 = 50.0 R26= 26.014 D26 = 5.75 R27 = −24.230 D27 = 1.50 N13 = 1.6200 ν13 = 60.3 R28= −56.688 D28 = 2.93 R29 = 47.995 D29 = 7.97 N14 = 1.5450 ν14 = 46.5 R30= −28.966 D30 = 1.80 N15 = 1.8850 ν15 = 41.0 R31 = −63.496 AsphericalCoefficient k B C D E 5th −4.36842E−01 2.38651E−08 3.19153E−135.47944E−15 4.24280E−19 Surface

(Third Numerical Embodiment) f = 294.0 Fno = 4.14 2ω = 8.42° R1 = ∞ D1 =3.30 N1 = 1.5860 ν1 = 58.6 R2 = ∞ D2 = 0.15 R3 = 118.585 D3 = 9.49 N2 =1.7581 ν2 = 51.0 R4 = −282.888 D4 = 0.39 NGNL1 = 1.7088 νGNL1 = 21.63 R5= −245.580 D5 = 0.05 NGL1 = 1.5963 νGL1 = 13.86 R6 = −304.535 D6 = 0.15R7 = 111.528 D7 = 6.25 N3 = 1.4870 ν3 = 70.4 R8 = 790.662 D8 = 5.08 R9 =−257.290 D9 = 3.40 N4 = 1.8571 ν4 = 25.3 R10 = 198.501 D10 = 0.15 R11 =51.772 D11 = 7.14 N5 = 1.4872 ν5 = 70.3 R12 = 122.949 D12 = 8.63 R13 =48.864 D13 = 3.00 N6 = 1.6224 ν6 = 60.1 R14 = 34.346 D14 = 10.96 R15 = ∞(Aperture Stop) D15 = 0.00 R16 = ∞ D16 = 4.00 R17 = 165.105 D17 = 3.24N7 = 1.7308 ν7 = 26.9 R18 = −171.100 D18 = 2.00 N8 = 1.8850 ν8 = 41.0R19 = 81.708 D19 = 33.04 R20 = 103.672 D20 = 1.60 N9 = 1.8500 ν9 = 23.0R21 = 27.632 D21 = 6.69 N10 = 1.6240 ν10 = 36.0 R22 = −55.631 D22 = 0.75R23 = ∞ D23 = 0.00 R24 = 73.585 D24 = 4.11 N11 = 1.8610 ν11 = 26.8 R25 =−50.590 D25 = 1.50 N12 = 1.7800 ν12 = 50.0 R26 = 25.300 D26 = 5.81 R27 =−27.223 D27 = 1.50 N13 = 1.7800 ν13 = 50.0 R28 = −56.849 D28 = 2.74 R29= 46.248 D29 = 7.00 N14 = 1.5348 ν14 = 49.2 R30 = −30.195 D30 = 2.38 N15= 1.8850 ν15 = 41.0 R31 = −70.012

(Fourth Numerical Embodiment) f = 294.0 Fno = 4.14 2ω = 8.42° R1 = ∞ D1= 3.30 N1 = 1.5860 ν1 = 58.6 R2 = ∞ D2 = 0.15 R3 = 155.141 D3 = 8.31 N2= 1.5797 ν2 = 62.6 R4 = −266.200 D4 = 1.50 NGNL1 = 1.6959 νGNL1 = 17.7R5 = −167.163 D5 = 0.05 NGL1 = 1.5425 νGL1 = 29.0 R6 = −220.744 D6 =0.15 R7 = 92.229 D7 = 7.11 N3 = 1.5387 ν3 = 65.5 R8 = 532.897 D8 = 3.14R9 = −269.965 D9 = 3.40 N4 = 1.8654 ν4 = 28.7 R10 = 130.581 D10 = 0.15R11 = 84.739 D11 = 8.54 N5 = 1.4873 ν5 = 70.4 R12 = −562.348 D12 = 19.08R13 = 41.082 D13 = 3.00 N6 = 1.4870 ν6 = 70.4 R14 = 36.019 D14 = 10.63R15 = ∞ (Aperture Stop) D15 = 0.00 R16 = ∞ D16 = 4.00 R17 = 169.956 D17= 3.76 N7 = 1.7498 ν7 = 26.2 R18 = −111.526 D18 = 2.00 N8 = 1.8819 ν8 =38.5 R19 = 81.708 D19 = 31.37 R20 = 93.664 D20 = 1.60 N9 = 1.8500 ν9 =23.0 R21 = 28.356 D21 = 6.58 N10 = 1.6279 ν10 = 42.0 R22 = −61.505 D22 =0.15 R23 = ∞ D23 = 0.00 R24 = 78.718 D24 = 6.43 N11 = 1.8610 ν11 = 26.8R25 = −42.700 D25 = 1.50 N12 = 1.7568 ν12 = 51.0 R26 = 24.842 D26 = 5.87R27 = −27.135 D27 = 1.50 N13 = 1.5906 ν13 = 61.9 R28 = −86.343 D28 =3.52 R29 = 45.811 D29 = 9.72 N14 = 1.5202 ν14 = 53.8 R30 = −29.816 D30 =3.00 N15 = 1.8850 ν15 = 41.0 R31 = −67.113

(Fifth Numerical Embodiment) f = 294.0 Fno = 4.14 2ω = 8.42° R1 = ∞ D1 =3.30 N1 = 1.5860 ν1 = 58.6 R2 = ∞ D2 = 0.15 R3 = 165.948 D3 = 9.02 N2 =1.4870 ν2 = 70.4 R4 = −189.026 D4 = 0.15 R5 = 107.153 D5 = 6.00 N3 =1.4870 ν3 = 70.4 R6 = 379.005 D6 = 1.50 NGNL1 = 1.5532 νGNL1 = 39.8 R7 =27779.873 (Aspherical D7 = 0.05 NGL1 = 1.7127 νGL1 = 13.8 R8 = 556.147Surface) D8 = 5.47 R9 = −242.960 D9 = 3.40 N4 = 1.8838 ν4 = 39.94 R10 =503.260 D10 = 1.11 R11 = 83.132 D11 = 7.39 N5 = 1.4870 ν5 = 70.4 R12 =1008.384 D12 = 17.33 R13 = 51.173 D13 = 3.00 N6 = 1.5115 ν6 = 64.0 R14 =40.513 D14 = 10.12 R15 = ∞ (Aperture Stop) D15 = 0.00 R16 = ∞ D16 = 4.00R17 = 177.678 D17 = 4.00 N7 = 1.7652 ν7 = 25.6 R18 = −105.297 D18 = 2.00N8 = 1.8823 ν8 = 38.8 R19 = 81.708 D19 = 32.54 R20 = 103.789 D20 = 1.60N9 = 1.8564 ν9 = 25.1 R21 = 34.769 D21 = 6.04 N10 = 1.6702 ν10 = 53.7R22 = −79.264 D22 = 0.15 R23 = ∞ D23 = 0.00 R24 = 49.645 D24 = 5.28 N11= 1.8585 ν11 = 26.3 R25 = −132.812 D25 = 1.50 N12 = 1.7276 ν12 = 52.5R26 = 23.745 D26 = 6.39 R27 = −41.576 D27 = 1.50 N13 = 1.6958 ν13 = 54.4R28 = 342.785 D28 = 4.04 R29 = 47.170 D29 = 7.53 N14 = 1.5269 ν14 = 51.6R30 = −30.301 D30 = 1.80 N15 = 1.8850 ν15 = 41.0 R31 = −67.490Aspherical Coefficient k B C D E 7th Surface 1.46158E+05 1.69205E−09−3.32770E−12 1.16835E−15 −5.92857E−19

(Sixth Numerical Embodiment) f = 294.0 Fno = 4.14 2ω = 8.42° R1 =157.370 D1 = 8.97 N1 = 1.5163 ν1 = 64.1 R2 = −204.567 D2 = 0.76 NGNL1 =1.6356 νGNL1 = 22.7 R3 = −168.921 D3 = 0.15 R4 = 96.414 D4 = 8.62 N2 =1.5638 ν2 = 60.7 R5 = −643.669 D5 = 0.05 NGL1 = 1.5425 νGL1 = 29.1 R6 =1526.834 D6 = 2.80 R7 = −228.046 D7 = 3.40 N3 = 1.8340 ν3 = 37.2 R8 =129.968 D8 = 0.73 R9 = 72.569 D9 = 8.93 N4 = 1.4875 ν4 = 70.2 R10 =5162.619 D10 = 13.48 R11 = 43.936 D11 = 3.50 N5 = 1.8052 ν5 = 25.4 R12 =37.942 D12 = 10.71 R13 = ∞ (Aperture Stop) D13 = 4.00 R14 = 139.290 D14= 4.00 N6 = 1.7215 ν6 = 29.2 R15 = −133.808 D15 = 2.00 N7 = 1.8830 ν7 =40.8 R16 = 81.708 D16 = 29.31 R17 = 133.715 D17 = 1.80 N8 = 1.8467 ν8 =23.8 R18 = 27.935 D18 = 8.13 N9 = 1.6668 ν9 = 33.1 R19 = −60.022 D19 =0.15 R20 = 90.843 D20 = 6.00 N10 = 1.8340 ν10 = 37.2 R21 = −39.347 D21 =2.30 N11 = 1.7725 ν11 = 49.6 R22 = 26.618 D22 = 5.82 R23 = −26.518 D23 =1.50 N12 = 1.4875 ν12 = 70.2 R24 = −107.094 D24 = 2.58 R25 = 50.997 D25= 9.00 N13 = 1.5481 ν13 = 45.8 R26 = −31.115 D26 = 3.00 N14 = 1.8830 ν14= 40.8 R27 = −64.669

(Seventh Numerical Embodiment) f = 24.5 Fno = 2.9 2ω = 82.9° R1 = 68.243D1 = 3.88 N1 = 1.6200 ν1 = 60.3 R2 = 252.730 D2 = 0.15 R3 = 41.127 D3 =1.00 N2 = 1.8850 ν2 = 41.0 R4 = 15.870 D4 = 7.54 R5 = 17.325 D5 = 2.68N3 = 1.8500 ν3 = 23.0 R6 = 23.812 D6 = 4.21 R7 = 24.185 D7 = 0.90 N4 =1.8567 ν4 = 25.2 R8 = 11.353 D8 = 2.28 R9 = 40.705 D9 = 2.50 N5 = 1.8524ν5 = 23.7 R10 = −104.354 D10 = 0.15 R11 = −198.801 D11 = 4.50 N6 =1.5153 ν6 = 67.5 R12 = 30.450 D12 = 4.68 R13 = ∞ (Aperture Stop) D13 =0.15 R14 = 33.576 D14 = 5.36 N7 = 1.7891 ν7 = 40.1 R15 = −19.804 D15 =2.82 R16 = −19.673 D16 = 4.00 N8 = 1.8500 ν8 = 23.0 R17 = 31.003 D17 =0.60 NGNL1 = 1.6356 νGNL1 = 22.7 R18 = 134.602 D18 = 0.05 NGL1 = 1.5425νGL1 = 29.1 R19 = 42.978 D19 = 1.11 R20 = −69.862 D20 = 2.46 N9 = 1.4870ν9 = 70.4 R21 = −16.976 D21 = 0.15 R22 = 2113.644 D22 = 2.82 N10 =1.6701 ν10 = 56.1 R23 = −25.957

TABLE 1 First Second Third Fourth Embodiment Embodiment EmbodimentEmbodiment Second Second First Second Second Optical Optical OpticalOptical Optical First Element First Element Element Element FirstElement Optical GL1 Optical GL1 GNL1 GL1 Optical GL1 Element 14.2%Element 14.2% 20% 20% Element 5% GNL1 ITO - GNL1 ITO - TiO2 - ITO - GNL1ITO - UV- UV- UV- UV- UV- UV- N- UV- Conditional curable curable curablecurable curable curable polyvinyl curable Expression resin 1 resin 2resin 1 resin 2 resin 2 resin 2 carbazole resin 2 Nd 1.6356 1.56481.6356 1.5648 1.7088 1.5963 1.6959 1.5425 Ng 1.6753 1.5941 1.6753 1.59411.7599 1.6383 1.7516 1.5630 NC 1.6281 1.5544 1.6281 1.5544 1.7003 1.58041.6853 1.5362 NF 1.6560 1.5826 1.6560 1.5826 1.7331 1.6234 1.7246 1.55495, 6 νd 22.73 20.03 22.73 20.03 21.63 13.86 17.68 29.05 θgd 1.42201.0362 1.4220 1.0362 1.5594 0.9761 1.4155 1.0963 θgF 0.6895 0.40690.6895 0.4069 0.8170 0.3459 0.6856 0.4346 3, 4 Δθgd 0.0826 −0.31510.0826 −0.3151 0.2152 −0.4049 0.0533 −0.2178 1, 2 ΔθgF 0.0652 −0.22720.0652 −0.2272 0.1888 −0.3130 0.0424 −0.1688 Fifth Sixth SeventhEmbodiment Embodiment Embodiment First First Second First Second OpticalSecond Optical Optical Optical Optical Element Optical Element ElementElement Element GNL1 Element GL1 GNL1 GL1 5% GNL1 GL1 5% 3% TiO2 - 10%ITO - N- UV- ITO - UV- UV- ITO - UV- Conditional UV-curable polyvinylcurable curable curable curable Expression resin 2 carbazole resin 1resin 2 resin 1 resin 2 Nd 1.5532 1.7127 1.6356 1.5425 1.6356 1.5425 Ng1.5725 1.7772 1.6753 1.5630 1.6753 1.5630 NC 1.5494 1.6969 1.6281 1.53621.6281 1.5362 NF 1.5633 1.7483 1.6560 1.5549 1.6560 1.5549 5, 6 νd 39.8113.85 22.73 29.05 22.73 29.05 θgd 1.3852 1.2527 1.4220 1.0963 1.42201.0963 θgF 0.6645 0.5604 0.6895 0.4346 0.6895 0.4346 3, 4 Δθgd 0.1063−0.1283 0.0826 −0.2178 0.0826 −0.2178 1, 2 ΔθgF 0.0898 −0.0986 0.0652−0.1688 0.0652 −0.1688

TABLE 2 UV Curable Resin 2 ITO TiO₂ Nd 1.52415 1.85712 2.30377 Ng1.53706 1.99244 2.45676 NC 1.52116 1.79794 2.28032 NF 1.53133 1.948702.37452 νd 51.55 5.69 13.84 θgd 1.269 0.898 1.624 θg, F 0.563 0.2900.873

TABLE 3 fGNL 1 fGL 1 fGNL 1 × fGL 1 First Embodiment 212.26 −1080.03−2.292E+05 Second Embodiment 854.15 −1291.92 −1.103E+06 Third Embodiment2589.31 −2118.06 −5.484E+06 Fourth Embodiment 641.66 −1269.85 −8.148E+05Fifth Embodiment 694.53 −796.27 −5.530E+05 Sixth Embodiment 1512.77−834.61 −1.263E+06 Seventh Embodiment 63.24 −116.40 −7.361E+03

An optical system according to an exemplary embodiment of the presentinvention is described below. The intersecting point of a light axis Laand a paraxial chief ray R is defined as “P”. This optical system is atelephoto optical system that is configured so that the maximum heightof the paraxial marginal ray from the light axis when the paraxialmarginal ray passes through the lens surface on the enlargement side ofthe point P is greater than that on the reduction side relative to thepoint P.

In the telephoto optical systems (optical systems having the total lenslength shorter than the focal length), a refractive optical element(hereinafter simply referred to as an “optical element”) composed of asolid material that has a positive or negative refractive power and thatsatisfies the following conditions is employed.

As used herein, the term “solid material” of the refractive opticalelement refers to a material that is solid in a use environment of theoptical system. Accordingly, the material may be in any state before theoptical system is in use (e.g., during a fabrication period). Forexample, even when the material is liquid during the fabrication period,the material is referred to as a “solid material” if the liquid materialis cured into a solid material.

FIG. 27 is a schematic illustration of a paraxial refractive powerarrangement for illustrating the optical function of the optical systemaccording to the present embodiment. As shown in FIG. 27, an opticalsystem OL is of a telephoto type having the total lens length (thedistance between the first lens surface and the image plane) that isshorter than the focal length. The telephoto optical system OL includesa front lens group Gp having a positive refractive power and a rear lensgroup Gn having a negative refractive power. The front lens group Gpincludes a first refractive optical element (a first optical element)GNL1 and a second refractive optical element (a second optical element)GL1 composed of a solid material that satisfies the followingconditional expressions (9) to (16). Hereinafter, the solid material issimply referred to as a “material”. For simplicity, all of the lensesincluded in the front lens group Gp and the rear lens group Gn are thinsingle lenses. These lenses are disposed along a light axis La in thefront lens group Gp and the rear lens group Gn so that the distancestherebetween are zero. In addition, each of the first refractive opticalelement GNL1 and the second refractive optical element GL is a thinsingle lens. The refractive optical system portion GNL and the secondrefractive optical element GL are disposed along the light axis La inthe front lens group Gp so that the distance therebetween is zero. Aparaxial marginal ray Q is a paraxial ray that, when the focal length ofthe entire optical system is normalized to “1”, travels parallel to thelight axis of the optical system at a height of “1” from the light axisand is made incident on the optical system. It is assumed that an objectis disposed on the left side of the optical system, and a light ray madeincident on the optical system from the object side travels from theleft to the right. A paraxial chief ray R is a paraxial ray that, whenthe focal length of the entire optical system is normalized to “1”,passes through an intersection between the entrance pupil and the lightaxis of the optical system among light rays made incident on the opticalsystem at an angle of −45° with respect to the light axis. The incidentangle of a ray is positive if the ray is measured from the light axis ina clockwise direction, while the incident angle is negative if the rayis measured from the light axis in a counterclockwise direction. Theintersecting point of the light axis La and a paraxial chief ray R isdefined as “P”. The image plane is denoted as “IP”.

As shown in FIG. 27, in the optical system OL, a maximum height h_(Gp)of the paraxial marginal ray Q from the light axis La when the paraxialmarginal ray Q passes through the lens surface on the enlargement side(the object side) is greater than a maximum height h_(Gn) of theparaxial marginal ray Q from the light axis La when the paraxialmarginal ray Q passes through the lens surface on the reduction side(the image side) relative to the point P. That is, H_(Gp) and H_(Gn)represent the heights of the paraxial chief ray R from the light axis Lawhen the paraxial chief ray R is made incident on the front lens groupGp and the rear lens group Gn, respectively.

The features of the optical system OL according to the present exemplaryembodiment are described next.

Let ft denote the focal length of the entire lens system, and Lt denotethe total lens length (the distance between the first lens surface andthe image plane).

As described above, let P denote the intersecting point of the lightaxis La and the paraxial chief ray R. The optical system OL includes afirst optical element GNL1 and a second optical element GL1 on at leastone of the enlargement side and the reduction side of the point P. Eachof the first optical element GNL1 and the second optical element GNL2has a refractive light incident surface and a refractive light emergentsurface and is made of a solid material.

Let ΔθgF1 and ΔθgF2 denote the anomalous partial dispersion values ofthe first optical element GNL1 and the second optical element GL1 forthe Fraunhofer g-line and F-line, respectively.

Let φ1 and φ2 denote the refractive powers of the first optical elementGNL1 and the second optical element GL1 when the incident and emergentsurfaces of the first optical element GNL1 and the second opticalelement GL1 are in contact with air.

Let ΔθgF1 and ΔθgF2 denote the anomalous partial dispersion values ofthe materials of the first optical element GNL1 and the second opticalelement GL1 for the Fraunhofer g-line and d-line, respectively.

Let νd1 and νd2 denote the Abbe numbers of the materials of the firstoptical element GNL1 and the second optical element GL1, respectively.

Then, at least one of the following conditional expressions issatisfied:

Lt/ft<1.0  (8)

ΔθgF1>0.0272  (9)

ΔθgF2<−0.0278  (10)

Δθgd1>0.038  (11)

Δθgd2<−0.037  (12)

νd1<60  (13)

νd2<60  (14)

φ1×φ2<0  (15)

(φ1×ΔθgF1/νd1)/(φ2×ΔθgF2/νd2)<1.5  (16)

For the optical element used in the optical system according to thepresent exemplary embodiment, the Abbe number νd, the relative partialdispersion θgd of the solid material for the Fraunhofer g-line andd-line, and the relative partial dispersion θgF of the solid materialfor the Fraunhofer g-line and F-line are defined as follows:

νd=(Nd−1)/(NF−NC)

θgd=(Ng−Nd)/(NF−NC)

θgF=(Ng−NF)/(NF−NC)

where Ng, NF, Nd, and NC denote the indices of refraction of the solidmaterial for the Fraunhofer g-line (435.8 nm), the Fraunhofer F-line(486.1 nm), the Fraunhofer d-line (587.6 nm), and the Fraunhofer C-line(656.3 nm), respectively.

In general, the relative partial dispersions θgd and θgF of the solidmaterial used for a lens system are approximated as follows:

θgd=−1.687×10⁻⁷ νd ³+5.702×10⁻⁵ νd ²−6.603×10⁻³ νd+1.462

θgF=−1.665×10⁻⁷ νd ³+5.213×10⁻⁵ νd ²−5.656×10⁻³ νd+0.7278

Here, the anomalous partial dispersion values Δθgd and ΔθgF areexpressed as follows:

Δθgd=θgd−(−1.687×10⁻⁷ νd ³+5.702×10⁻⁵ νd ²−6.603×10⁻³ νd+1.462)

ΔθgF=θgF−(−1.665×10⁻⁷ νd ³+5.213×10⁻⁵ νd ²−5.656×10⁻³ νd+0.7278)

According to the present exemplary embodiment, the optical system OLincludes at least one first refractive optical element GNL1 that iscomposed of a solid material having high dispersion and high relativepartial dispersion and at least one second refractive optical elementGL1 that is composed of a solid material having high dispersion and lowrelative partial dispersion.

As used herein, the term “refractive optical element” refers to anoptical element, such as a refractive lens, that produces refractivepower using a refracting effect. Thus, a diffractive optical elementthat produces refractive power using a diffracting effect is notincluded in the category of the term “refractive optical element”.

The optical systems of the exemplary embodiments are telephoto opticalsystems that satisfy conditional expression (8).

According to the exemplary embodiments, by employing at least one firstrefractive optical element GNL1 composed of a solid material thatsatisfies conditional expression (9) and at least one second refractiveoptical element GL1 composed of a solid material that satisfiesconditional expression (10), chromatic aberration of the optical systemin the entire wavelength range of visible light can be sufficientlycorrected.

By employing solid materials having anomalous partial dispersion valuesthat satisfy conditional expressions (11) and (12), chromatic aberrationof the optical system in the range of a short wavelength (400 nm) to amedium wavelength (550 nm) can be sufficiently corrected. In addition,chromatic aberration of the optical system in a wide range of a shortwavelength to a long wavelength (700 nm) can be further sufficientlycorrected.

By employing solid materials having the Abbe numbers that satisfyconditional expressions (13) and (14), chromatic aberration of theoptical system can be easily corrected.

By configuring the first optical element GNL1 and the second opticalelement GL1 so that the first optical element GNL1 and the secondoptical element GL1 have refractive powers that satisfy conditionalexpression (15), chromatic aberration of the optical system in a widewavelength range can be sufficiently corrected.

In addition, by configuring the first optical element GNL1 and thesecond optical element GL1 so that conditional expression (16) issatisfied, the optical system can sufficiently correct chromaticaberration mostly occurring in telephoto optical systems.

In the exemplary embodiments, when the first optical element GNL1 andthe second optical element GL1 are provided in the optical system, it isdesirable that both the first optical element GNL1 and the secondoptical element GL1 are disposed on the enlargement side relative to thepoint P at which the light axis La intersects the paraxial chief ray R.

Examples of the solid material (optical material) that satisfiesconditional expression (9) include a variety of resins. Among thevariety of resins, a UV-curable resin (Nd=1.635, νd=22.7, and θgF=0.69)and N-polyvinyl carbazole (Nd=1.696, νd=17.7, and θgF=0.69) are opticalmaterials that satisfy conditional expression (9). However, in additionto these materials, any solid material that satisfies conditionalexpression (9) can be employed.

In addition, an optical material having a characteristic that isdifferent from that of a widely used glass material can be used.Examples of such an optical material include a mixture of a syntheticresin and inorganic oxide nanoparticles dispersed therein. Examples ofthe inorganic oxide nanoparticles include TiO₂ particles (Nd=2.304 andνd=13.8), Nb₂O₅ particles (Nd=2.367 and νd=14.0), ITO particles(Nd=1.8571 and νd=5.69), CrO₃ particles (Nd=2.2178 and νd=13.4), andBaTiO₃ particles (Nd=2.4362 and νd=11.3).

Among these types of inorganic oxide, by dispersing TiO₂ particles(Nd=2.304, νd=13.8, and θgF=0.87) in a synthetic resin in an appropriatevolume ratio, an optical material that satisfies conditional expression(9) can be obtained.

In addition, by dispersing ITO fine particles (Nd=1.8571, νd=5.69, andθgF=0.873) in a synthetic resin in an appropriate volume ratio, anoptical material that satisfies conditional expression (10) can beobtained. However, in addition to the above-described materials, anysolid material that satisfies conditional expression (10) can beemployed.

In the exemplary embodiments, by using an optical material having arelative partial dispersion higher than that of a widely used opticalmaterial and an optical material having a relative partial dispersionlower than that of a widely used optical material, chromatic aberrationis sufficiently corrected.

In the wavelength-dependent characteristic of the index of refraction(dispersion characteristic) of an optical material, the Abbe numberrepresents the slope of the dispersion characteristic curve, and therelative partial dispersion represents the curvature of the dispersioncharacteristic curve.

In general, the index of refraction of an optical material in ashort-wavelength range is higher than that in a long-wavelength range.At that time, the Abbe number and the relative partial dispersion arepositive.

Accordingly, the dispersion characteristic curve is downwardly convex. Achange in the index of refraction relative to a change in the wavelengthincreases towards a short-wavelength range. For example, refractiveindex characteristics with respect to a wavelength for S-BSL7 (Nd=1.516and νd=64.1) and S-TIH53 (Nd=1.847 and νd=23.8) available from OHARAcorporation are shown in FIG. 41.

In addition, a high-dispersion optical material having a smaller Abbenumber tends to have a higher relative partial dispersion for the g-lineand F-line and a higher relative partial dispersion for the g-line andd-line.

In widely used optical materials, the relative partial dispersionsubstantially linearly changes with respect to the Abbe number. However,an optical material having an anomalous partial dispersion changesdifferently from the linear change. A typical example of such ananomalous partial dispersion material is fluorite.

The wavelength-dependent characteristic curve of a chromatic aberrationcoefficient of an optical material having a high relative partialdispersion has a large curvature in a short-wavelength range, comparedwith that of a widely used optical material.

When the refractive power of the lens surface of an optical materialhaving a high relative partial dispersion is changed in order to controlthe chromatic aberration, the slope of the entire wavelength-dependentcharacteristic curve of a chromatic aberration coefficient changes suchthat the entire wavelength-dependent characteristic curve rotates abouta point of a reference design wavelength. In particular, the change issignificant in a short-wavelength range for an optical material having ahigh relative partial dispersion. As a result, the slope of the entirewavelength-dependent characteristic curve is changed while significantlychanging the curvature in the short-wavelength range.

By using this property, the curvature of the wavelength-dependentcharacteristic curve of a chromatic aberration coefficient in theshort-wavelength range can be canceled. However, it is difficult tocorrect the remaining slope of the wavelength-dependent characteristiccurve of a chromatic aberration coefficient at the same time. Inaddition, the correction of the curvature in the short-wavelength rangerelatively increases chromatic aberration in a long-wavelength range. Toprevent the increase in chromatic aberration in a long-wavelength range,the refractive power of an appropriate one of the glass surfaces of theoptical system needs to be changed. However, this is not suitable forcorrecting a variety of aberrations other than chromatic aberration.

In contrast, the wavelength-dependent characteristic curve of achromatic aberration coefficient of an optical material having a lowrelative partial dispersion has a small curvature in a short-wavelengthrange. Accordingly, the chromatic aberration coefficient linearlychanges with a change in wavelength, compared with that of a widely usedoptical material. When the refractive power of the lens surface of anoptical material having a low relative partial dispersion is changed inorder to control the chromatic aberration, the slope of the entirewavelength-dependent characteristic curve of a chromatic aberrationcoefficient changes such that the entire wavelength-dependentcharacteristic curve rotates about a point of a reference designwavelength while relatively retaining linearity with respect to thewavelength. In this way, the slope of the wavelength-dependentcharacteristic curve of a chromatic aberration coefficient can becorrected.

Accordingly, by employing an optical material having a low relativepartial dispersion in addition to an optical material having a highrelative partial dispersion, the curvature of the wavelength-dependentcharacteristic curve of a chromatic aberration coefficient in ashort-wavelength range and the slope of the entire wavelength-dependentcharacteristic curve can be corrected at the same time. That is, thechromatic aberration of the optical system can be sufficiently correctedin a wide wavelength range of the g-line to C-line.

Such correction of chromatic aberration of a telephoto lens is describednext with reference to a telephoto lens including a refractive opticalsystem portion GNL using an optical material having a high relativepartial dispersion, a refractive optical system portion GL using anoptical material having a low relative partial dispersion, and arefractive optical system portion G using a widely used optical materialhaving a normal relative partial dispersion.

Chromatic aberration of the refractive optical system portion G iscorrected to some extent first. Then, a relatively high-dispersionoptical material is selected for a negative lens included in therefractive optical system portion G. In this case, the slope of theentire wavelength-dependent characteristic curve of a chromaticaberration coefficient of the refractive optical system portion G ischanged while the portion in a short-wavelength range is significantlycurved from the original shape.

At that time, an appropriate refractive power is provided to therefractive optical system portion GNL, and a relatively high-dispersionoptical material is selected for a positive lens included in therefractive optical system portion G. However, in the case where therefractive optical system portion GNL is composed of a widely usedoptical material having a uniform relative partial dispersion withrespect to an Abbe number, the refractive optical system portion GNL ispartially responsible equally for a curvature component and a slopecomponent of the wavelength-dependent characteristic curve of achromatic aberration coefficient of the refractive optical systemportion G. Therefore, the curvature component and the slope componentcannot be canceled at the same time.

In contrast, in the case where the refractive optical system portion GNLis composed of an optical material having a relative partial dispersionhigher than that of a widely used optical material, the refractiveoptical system portion GNL is relatively largely responsible for theslope component of the entire wavelength-dependent characteristic curveof a chromatic aberration coefficient of the main refractive opticalsystem portion G. Therefore, the curvature component can be mainlycanceled. As a result, the slope of the entire wavelength-dependentcharacteristic curve of a chromatic aberration coefficient can bechanged while increasing linearity from the original shape.

At that time, by further providing the refractive optical system portionGL with an appropriate refractive power with a plus/minus sign oppositeto that of the refractive optical system portion GNL, the slope of theentire wavelength-dependent characteristic curve of a chromaticaberration coefficient of the refractive optical system portion G can becorrected.

However, if the refractive optical system portion GL is composed of awidely used optical material, the refractive optical system portion GLhas a characteristic in which the wavelength-dependent characteristiccurve of a chromatic aberration coefficient is relatively largely convexin a direction opposite to that corresponding to thewavelength-dependent characteristic curve of the refractive opticalsystem portion G. Accordingly, although the slope component of theentire wavelength-dependent characteristic curve of a chromaticaberration coefficient can be canceled, a curvature component thatincreases the chromatic aberration occurs.

At that time, to correct the curvature component of the entirewavelength-dependent characteristic curve of a chromatic aberrationcoefficient, the refractive power of the refractive optical systemportion GNL composed of a material having a high relative partialdispersion needs to be further changed. However, if the refractive poweris further changed, the thickness of the lens in the light axisdirection disadvantageously increases.

In contrast, in the case where the refractive optical system portion GLis composed of an optical material having a low relative partialdispersion, linearity of the wavelength-dependent characteristic curveof a chromatic aberration coefficient of the refractive optical systemportion GL is relatively increased. That is, by changing the refractivepower of the refractive optical system portion GL in order to correctthe chromatic aberration, the slope of the wavelength-dependentcharacteristic curve of a chromatic aberration coefficient can bechanged so that the wavelength-dependent characteristic curve rotatesabout the point of the design reference wavelength while substantiallymaintaining linearity. Accordingly, the chromatic aberration can besufficiently corrected.

As described above, by using the refractive optical system portion GNLand the refractive optical system portion GL for the main refractiveoptical system portion G, the slope component and the curvaturecomponent of the wavelength-dependent characteristic curve of achromatic aberration coefficient can be relatively easily corrected atthe same time.

To sufficiently correct chromatic aberration by using one of therefractive optical system portion GNL and the refractive optical systemportion GL, the refractive power of a lens surface of one of therefractive optical system portion GNL and the refractive optical systemportion GL and the refractive power of a lens surface of the refractiveoptical system portion G need to be increased.

That is, by employing the refractive optical system portions GNL and GL,the refractive power of each of the refractive optical system portionGNL and the refractive optical system portion GL can be relativelyreduced. As a result, the thickness of the solid material in the lightaxis direction can be reduced. Furthermore, by employing the refractiveoptical system portions GNL and GL, the chromatic aberration can bereduced without significantly changing the refractive power of therefractive optical system portion G. Accordingly, a variety ofaberrations other than the chromatic aberration can be maintainedunchanged.

At that time, to independently correct chromatic aberration, it isdesirable that the refractive optical system portion GNL and therefractive optical system portion GL are composed of an optical materialhaving a small Abbe number, that is, a high-dispersion optical material.Furthermore, in the telephoto optical system, it is desirable that atleast one refractive optical system portion GNL and at least onerefractive optical system portion GL are disposed on the enlargementside relative to the point P at which the paraxial chief ray intersectsthe light axis.

This is described in detail next with reference to an axial chromaticaberration coefficient and a chromatic aberration coefficient ofmagnification of a lens surface.

Let ΔΨ denote a change in refractive power of a surface of a refractivelens, and ν denote the Abbe number. Let h and H denote the heights ofthe paraxial marginal ray and the paraxial chief ray from the light axiswhen the paraxial marginal ray and the paraxial chief ray pass throughthe surface of the refractive lens. Then, a change ΔL in the axialchromatic aberration coefficient and a change ΔT in a chromaticaberration coefficient of magnification can be expressed as follows:

ΔL=h ²·ΔΨ/ν  (a)

ΔT=h·H·ΔΨ/ν  (b)

As can be seen from equations (a) and (b), the changes in theseaberration coefficients with respect to a change in the refractive powerof the lens surface increase as the absolute number of the Abbe numberdecreases (i.e., as the dispersion increases). Accordingly, by using ahigh-dispersion material having a small absolute number of the Abbenumber, the change amount of the refractive power that is required forobtaining a desired chromatic aberration can be reduced.

According to an aberration theory, this allows the chromatic aberrationto be controlled without significantly affecting the sphericalaberration, coma aberration, and astigmatism aberration. Thus, thechromatic aberration can be highly independently controlled.

In contrast, if a low-dispersion material is employed, the change amountof the refractive power that is required for obtaining a desiredchromatic aberration is increased. With the increase in the changeamount of the refractive power, a variety of aberrations, such asspherical aberration, significantly change. Thus, the chromaticaberration cannot be independently controlled. Therefore, in order tocorrect aberrations, it is important that, among the lenses of theoptical system, at least one of the surfaces of the lenses is a surfaceof a refractive lens made of a high-dispersion material.

In addition, equations (a) and (b) indicate that the changes in theaxial chromatic aberration coefficient ΔL and the chromatic aberrationcoefficient of magnification ΔT are determined by the values of theheights h and H. Using this result, the optimal arrangement of therefractive optical system portion GNL and the refractive optical systemportion GL in the optical system is described next.

To sufficiently correct chromatic aberration, the slope component andthe curvature components of the wavelength-dependent characteristiccurve of a chromatic aberration coefficient need to be corrected at thesame time. However, if the refractive power change ΔΨ is decreased,sufficient correction of the chromatic aberration cannot be achieved. Incontrast, if the refractive power change ΔΨ is increased, the thicknessof an optical element (i.e., a lens) is increased.

In general, since the transmittance of the optical material of therefractive optical system portion GNL and the refractive optical systemportion GL having an anomalous partial dispersion characteristic is low,the thickness of a lens composed of the optical material needs to berelatively reduced when the refractive optical system portions are usedfor lenses. In addition, as the thickness decreases, a change in theoptical performance with a change in the surrounding environmentdecreases. Accordingly, the resistance to the surrounding environmentincreases.

That is, in order to reduce the thicknesses of the refractive opticalsystem portion GNL and the refractive optical system portion GL andsufficiently correct the chromatic aberration, it is desirable that thecorrection amounts of the slope component and the curvature component ofthe wavelength-dependent characteristic curve of a chromatic aberrationcoefficient are appropriately controlled. According to equations (a) and(b), the correction amounts are determined by the heights h and H.Accordingly, the correction amounts change in accordance with thepositions of the refractive optical system portions GNL and GL in theoptical system. That is, in order to sufficiently correct the chromaticaberration and reduce the change amounts of the refractive powers of therefractive optical system portions GNL and GL, it is important to selectthe appropriate positions at which the refractive optical systemportions GNL and GL are disposed.

The appropriate positions of the refractive optical system portions GNLand GL at which the chromatic aberration is sufficiently corrected andthe change amounts of the refractive powers are reduced depend on theaberration structure of the optical system. In addition, the aberrationstructure varies in accordance with the type of optical system.

For the telephoto optical systems according to the exemplaryembodiments, the refractive optical system portions GNL and GL can bedisposed on the enlargement side relative to the point P. Thisarrangement can sufficiently correct axial chromatic aberration andchromatic aberration of magnification. Furthermore, by letting theoptical characteristics of the refractive optical system portions GNLand GL satisfy conditional expression (16), axial chromatic aberrationand chromatic aberration of magnification can be corrected at the sametime, and the curvature component and the slope component of thewavelength-dependent characteristic curve of a chromatic aberrationcoefficient can be further sufficiently corrected.

At that time, in order to cancel the curvature component and the slopecomponent of the wavelength-dependent characteristic curve of achromatic aberration coefficient, the product (φ1×φ2) of the refractivepower of the refractive optical system portion GNL (φ1) and therefractive power of the refractive optical system portion GL (φ2) can benegative, as indicated by conditional expression (15). This is due tothe wavelength-dependent characteristic of chromatic aberration of thetelephoto optical system.

It is more desirable that the following conditions are satisfied: φ1>0and φ2<0.

In general, when a lens group is moved in order to perform zooming andfocusing and control the position of the image, the states of a ray madeincident on the lens groups change, and therefore, aberrations occurringin the lens groups change. Accordingly, in order to sufficiently correctthe aberrations of the entire optical system in all the use cases,aberration coefficients that simultaneously change in all the use casesneed to be determined for each of the lens groups. By disposing therefractive optical system portions GNL and GL in the same lens group,desired aberration values can be easily obtained.

In addition, if the thicknesses of the refractive optical systemportions GNL and GL are reduced, a change in the characteristic due tothe surrounding environment is reduced. Furthermore, by satisfyingconditional expression (15), the changes in the characteristics of therefractive optical system portions GNL and GL cancel each other out.Therefore, the resistance to the surrounding environment can beincreased.

A variety of aberrations including chromatic aberration are corrected bythe refractive optical system portions GNL and GL in cooperation with awidely used optical material. Accordingly, the characteristics of therelative partial dispersions of the refractive optical system portionsGNL and GL need to be different from that of the widely used opticalmaterial in order to correct the aberrations. However, a stronganomalous partial dispersion should be avoided.

When a lens made of an optical material having a characteristicsignificantly different from that of a widely used optical material isemployed, the curvature of the wavelength-dependent characteristic curveof a chromatic aberration coefficient of the lens surface isparticularly large. To correct the large curvature component, therefractive powers of other lenses need to be increased. This givessignificant impact on the spherical aberration, the coma aberration, andthe astigmatism aberration. Thus, it is difficult to correct theseaberrations.

That is, the material of the refractive optical system portion GNL needsto be an optical material having a relative partial dispersion higherthan that of a widely used optical material, but not having a relativepartial dispersion significantly different from that of a widely usedoptical material.

To obtain further sufficient correction of chromatic aberration, therange of the anomalous partial dispersion value ΔθgF1 defined byconditional expression (9) can be redefined as follows:

0.0272<ΔθgF1<0.2832  (9a)

To obtain still further sufficient correction of chromatic aberration,the range of the anomalous partial dispersion value ΔθgF1 defined byconditional expression (9a) can be redefined as follows:

0.0342<ΔθgF1<0.2832  (9b)

To obtain further sufficient correction of chromatic aberration, therange of the anomalous partial dispersion value ΔθgF2 defined byconditional expression (10) can be redefined as follows:

−0.4278<ΔθgF2<−0.0528  (10a)

To obtain still further sufficient correction of chromatic aberration,the range of the anomalous partial dispersion value ΔθgF2 defined byconditional expression (10a) can be redefined as follows:

−0.4278<ΔθgF2<−0.0778  (10b)

To obtain further sufficient correction of chromatic aberration, therange of the anomalous partial dispersion value Δθgd1 defined byconditional expression (11) can be redefined as follows:

0.038<Δθgd1<0.347  (11a)

To obtain still further sufficient correction of chromatic aberration,the range of the anomalous partial dispersion value Δθgd1 defined byconditional expression (11a) can be redefined as follows:

0.051<Δθgd1<0.347  (11b)

To obtain further sufficient correction of chromatic aberration, therange of the anomalous partial dispersion value Δθgd2 defined byconditional expression (12) can be redefined as follows:

−0.5620<Δθgd2<−0.062  (12a)

To obtain still further sufficient correction of chromatic aberration,the range of the anomalous partial dispersion value Δθgd1 defined byconditional expression (12a) can be redefined as follows:

−0.5620<Δθgd2<−0.112  (12b)

To obtain further sufficient correction of chromatic aberration, theranges of the Abbe numbers νd1 and νd2 defined by conditionalexpressions (13) and (14) can be redefined as follows:

νd1<50  (13a)

νd2<50  (14a)

To obtain still further sufficient correction of chromatic aberration,the ranges of the Abbe numbers νd1 and νd2 defined by conditionalexpressions (13a) and (14a) can be redefined as follows:

νd1<45  (13b)

νd2<45  (14b)

To obtain yet still further sufficient correction of chromaticaberration, the ranges of the Abbe numbers νd1 and νd2 defined byconditional expressions (13b) and (14b) can be redefined as follows:

νd1<40  (13c)

νd2<40  (14c)

In the exemplary embodiments, the optical elements GNL1 and GL1 made ofoptical materials that satisfy conditional expressions (9) and (10) areemployed for a lens and a refractive layer provided on a lens of theoptical system. In addition, if the refractive surface composed of suchan optical material is aspherical, chromatic aberration flare, such asspherical aberration of a color, can be corrected. Furthermore, if aninterface is formed between the optical element and air atmosphere orbetween the optical element and an optical material having a relativelylow index of refraction, the chromatic aberration can be relativelysignificantly changed by slightly changing the radius of curvature ofthe interface.

Exemplary embodiments in which an optical element composed of theoptical material that satisfies at least one of conditional expressions(9) to (16) is employed for an optical system that satisfies conditionalexpression (8) are described in detail next. In these exemplaryembodiments, a UV-curable resin 1, N-polyvinyl carbazole, or a mixtureof a UV-curable resin 2 and TiO₂ fine particles dispersed therein isused for an optical material that satisfies conditional expressions (9),(11), and (13). A mixture of the UV-curable resin 2 and ITO fineparticles dispersed therein or a mixture of N-polyvinyl carbazole andITO fine particles dispersed therein is used for an optical materialthat satisfies conditional expressions (10), (12), and (14).

An optical system for use in each of the exemplary embodiments is atelephoto lens system used in an image pickup apparatus, such as a videocamera, a digital camera, or a silver-halide film camera. In thecross-sectional views of lenses, an object is located on the left side(the front side), and an image plane is located on the right side (therear side).

In the case where the optical systems of the exemplary embodiments areused for projection lenses of, for example, projectors, a screen islocated on the left side, and an image to be projected is located on theright side.

In the cross-sectional views of lenses, “i” represents the order of alens group numbered from the object. “Li” represents an ith lens group.

In addition, “SP” represents an aperture stop. “IP” represents an imageplane. When the optical system is used for a photo-taking lens of avideo camera or a digital still camera, an imaging surface of asolid-state image pickup element (a photoelectric conversion element),such as a CCD sensor or a CMOS sensor, is disposed in the image planeIP. When the optical system is used for a photo-taking lens of asilver-halide film camera, a light-sensitive surface corresponding tothe film surface is disposed in the image plane IP.

In aberration diagrams, “d” and “g” represent the d-line and g-line,respectively. “ΔM” and “ΔS” represent the meridional image plane and thesagittal image plane, respectively. The chromatic aberration ofmagnification is represented using the g-line. “ω” denotes the halfangle of field. “Fno” denotes the F number.

According to an eighth exemplary embodiment, as shown in FIG. 15, anoptical system is a telephoto lens having a focal length of 400 mm. Theoptical system includes a first lens group L1 having a positiverefractive power, a second lens group L2 having a negative refractivepower, and a third lens group L3 having a positive refractive power.When focusing is carried out, the first lens group L1 is stationary, thesecond lens group L2 is moved along the light axis, and the third lensgroup L3 is stationary.

In this optical system, the first lens group L1 includes the first andsecond optical elements.

According to the present embodiment, the optical system includes a lens(a first optical element) GNL1 composed of the UV-curable resin 1 and alens (a second optical element) GL1 composed of a mixture of theUV-curable resin 2 and 14.2% by volume ITO fine particles dispersedtherein.

As shown in FIG. 15, the first optical element GNL1 is a lens (layer)composed of the UV-curable resin 1 and having a positive refractivepower. The second optical element GL1 is a lens (layer) composed of amixture including ITO fine particles and having a negative refractivepower.

According to the eighth embodiment, the first lens group L1 includes thelens (layer) GNL1 and the lens (layer) GL1 on the object side where,when the paraxial marginal ray passes through the first lens group L1,the height of the paraxial marginal ray from the light axis isrelatively large. In addition, the lens GNL1 and the lens GL1 are intight contact with each other. The contact surface is aspherical. Thelens GNL1 and the lens GL1 are cemented between the other lenses. Inthis way, axial chromatic aberration and chromatic aberration ofmagnification are sufficiently corrected. Thus, a compact telephoto lenshaving a telephoto ratio of 0.764 can be achieved.

According to a ninth exemplary embodiment, as shown in FIG. 17, theoptical system is a telephoto lens having a focal length of 300 mm. Theoptical system includes a first lens group L1 having a positiverefractive power, a second lens group L2 having a negative refractivepower, and a third lens group L3 having a positive refractive power.When focusing is carried out, the first lens group L1 is stationary, thesecond lens group L2 is moved along the light axis, and the third lensgroup L3 is stationary.

According to the present exemplary embodiment, the optical systemincludes a lens (a first optical element) GNL1 composed of theUV-curable resin 1 and a lens (a second optical element) GL1 composed ofa mixture of the UV-curable resin 2 and 14.2% by volume ITO fineparticles dispersed therein. The lens (layer) GNL1 composed of theUV-curable resin 1 is a lens (layer) having a positive refractive power.The lens (layer) GL1 composed of the mixture including ITO fineparticles is a lens (layer) having a negative refractive power.

According to the ninth embodiment, the first lens group L1 includes thelens (layer) GNL1 and the lens (layer) GL1 on the object side where,when the paraxial marginal ray passes through the first lens group L1,the height of the paraxial marginal ray from the light axis isrelatively large. In addition, the lens GNL1 is in tight contact withthe lens GL1. The contact surface is aspherical. In this way, axialchromatic aberration and chromatic aberration of magnification aresufficiently corrected. Thus, a compact telephoto lens having atelephoto ratio of 0.669 can be achieved.

According to a tenth exemplary embodiment, as shown in FIG. 19, theoptical system is a telephoto lens having a focal length of 300 mm. Theoptical system includes a first lens group L1 having a positiverefractive power, a second lens group L2 having a negative refractivepower, and a third lens group L3 having a positive refractive power.When focusing is carried out, the first lens group L1 is stationary, thesecond lens group L2 is moved along the light axis, and the third lensgroup L3 is stationary.

According to the present exemplary embodiment, the optical systemincludes a lens (a first optical element) GNL1 composed of a mixture ofthe UV-curable resin 2 and 20% by volume TiO₂ fine particles dispersedtherein. The optical system further includes a lens (a second opticalelement) GL1 composed of a mixture of the UV-curable resin 2 and 20% byvolume ITO fine particles dispersed therein. The lens (layer) GNL1composed of the mixture including TiO₂ fine particles is a lens (layer)having a positive refractive power. The lens (layer) GL1 composed of themixture including ITO fine particles is a lens (layer) having a negativerefractive power.

According to the tenth embodiment, the first lens group L1 includes thelens (layer) GNL1 and the lens (layer) GL1 on the object side where,when the paraxial marginal ray passes through the first lens group L1,the height of the paraxial marginal ray from the light axis isrelatively large. In this way, axial chromatic aberration and chromaticaberration of magnification are sufficiently corrected. Thus, a compacttelephoto lens having a telephoto ratio of 0.669 can be achieved.

According to an eleventh exemplary embodiment, as shown in FIG. 21, theoptical system is a telephoto lens having a focal length of 300 mm. Theoptical system includes a first lens group L1 having a positiverefractive power, a second lens group L2 having a negative refractivepower, and a third lens group L3 having a positive refractive power.When focusing is carried out, the first lens group L1 is stationary, thesecond lens group L2 is moved along the light axis, and the third lensgroup L3 is stationary.

According to the present exemplary embodiment, the optical systemincludes a lens (a first optical element) GNL1 composed of N-polyvinylcarbazole and a lens (a second optical element) GL1 composed of amixture of the UV-curable resin 2 and 5% by volume ITO fine particlesdispersed therein. The lens (layer) GNL1 composed of N-polyvinylcarbazole is a lens (layer) having a positive refractive power. The lens(layer) GL1 composed of the mixture including ITO fine particles is alens (layer) having a negative refractive power.

According to the eleventh embodiment, the first lens group L1 includesthe lens (layer) GNL1 and the lens (layer) GL1 on the object side where,when the paraxial marginal ray passes through the first lens group L1,the height of the paraxial marginal ray from the light axis isrelatively large. In this way, axial chromatic aberration and chromaticaberration of magnification are sufficiently corrected. Thus, a compacttelephoto lens having a telephoto ratio of 0.720 can be achieved.

According to a twelfth exemplary embodiment, as shown in FIG. 23, theoptical system is a telephoto lens having a focal length of 300 mm. Theoptical system includes a first lens group L1 having a positiverefractive power, a second lens group L2 having a negative refractivepower, and a third lens group L3 having a positive refractive power.When focusing is carried out, the first lens group L1 is stationary, thesecond lens group L2 is moved along the light axis, and the third lensgroup L3 is stationary.

According to the present exemplary embodiment, the optical systemincludes a lens (a first optical element) GNL1 composed of a mixture ofthe UV-curable resin 2 and 3% by volume TiO₂ fine particles dispersedtherein. The optical system further includes a lens (a second opticalelement) GL1 composed of a mixture of N-polyvinyl carbazole and 10% byvolume ITO fine particles dispersed therein. The lens (layer) GNL1composed of the mixture including TiO₂ fine particles is a lens (layer)having a positive refractive power. The lens (layer) GL1 composed of themixture including ITO fine particles is a lens (layer) having a negativerefractive power.

According to the twelfth embodiment, the first lens group L1 includesthe lens (layer) GNL1 and the lens (layer) GL1 on the object side where,when the paraxial marginal ray passes through the first lens group L1,the height of the paraxial marginal ray from the light axis isrelatively large. In this way, axial chromatic aberration and chromaticaberration of magnification are sufficiently corrected. Thus, a compacttelephoto lens having a telephoto ratio of 0.748 can be achieved.

According to a thirteenth exemplary embodiment, as shown in FIG. 25, theoptical system is a telephoto lens having a focal length of 300 mm. Theoptical system includes a first lens group L1 having a positiverefractive power, a second lens group L2 having a negative refractivepower, and a third lens group L3 having a positive refractive power.When focusing is carried out, the first lens group L1 is stationary, thesecond lens group L2 is moved along the light axis, and the third lensgroup L3 is stationary.

According to the present exemplary embodiment, the optical systemincludes a lens (a first optical element) GNL1 composed of theUV-curable resin 1 and a lens (a second optical element) GL1 composed ofa mixture of the UV-curable resin 2 and 5% by volume ITO fine particlesdispersed therein. The lens (layer) GNL1 composed of the UV-curableresin 1 is a lens (layer) having a positive refractive power. The lens(layer) GL1 composed of the mixture including ITO fine particles is alens (layer) having a negative refractive power.

According to the thirteenth embodiment, the first lens group L1 includesthe lens (layer) GNL1 and the lens (layer) GL1 on the object side where,when the paraxial marginal ray passes through the first lens group L1,the height of the paraxial marginal ray from the light axis isrelatively large. In this way, axial chromatic aberration and chromaticaberration of magnification are sufficiently corrected. Thus, a compacttelephoto lens having a telephoto ratio of 0.737 can be achieved.

Particular values used in eighth to thirteenth numerical embodiments,which correspond to the eighth to thirteenth exemplary embodiments, aredescribed below. In the following numerical embodiments, i denotes theorder of a surface numbered from the object. Ri denotes the radius ofcurvature of the ith optical surface, and Di denotes a distance betweenthe ith surface and the (i+1)th surface along the light axis. Ni and videnote the index of refraction and the Abbe number of a material of theith optical element (excluding a lens (layer) composed of a resin, amaterial including TiO₂ fine particles dispersed therein, or a materialincluding ITO fine particles dispersed therein) for the d-line,respectively. NGNLj and vGNLj denote the index of refraction and theAbbe number of a material of a lens GNLj composed of a resin, a materialincluding TiO₂ fine particles dispersed therein, or a material includingITO fine particles dispersed therein for the d-line, respectively. Here,j=1, 2, . . . “f” denotes the focal length of an optical system. “Fno”denotes the F number. “ω” denotes the half angle of field.

The shape of an aspherical surface is expressed by the followingequation:

${x(h)} = {\frac{\left( {1/r} \right)h^{2}}{1 + \sqrt{\left\{ {1 - {\left( {1 + k} \right)\left( {h/r^{2}} \right)}} \right\}}} + {B\; h^{4}} + {C\; h^{6}} + {D\; h^{8}} + {E\; h^{10}} + \ldots}$

where

X is an amount of displacement from the surface vertex in the light axisdirection,

h is a height from the light axis in a direction perpendicular to thelight axis,

r is the paraxial radius of curvature,

k is the conic constant, and

B, C, D, E, . . . are aspherical coefficients at respective orders.

In Table 6 and in each aspherical coefficient, “E±XX” means “×10^(±XX)”.

Table 4 shows the indices of refraction, the Abbe numbers, the relativepartial dispersions, and the refractive powers of the refractive opticalsystem portions GNL1 and GL1 for the d-line, g-line, C-line, and F-line,and values for conditional expression (8) in each numerical embodiment.Table 5 shows the indices of refraction, the Abbe numbers, and therelative partial dispersions of the UV-curable resin 2, ITO, and TiO₂for the d-line, g-line, C-line, and F-line. Table 6 shows the values ofthe refractive optical elements GNLj and GLj for conditional expression(16) in each numerical embodiment.

(Eighth Numerical Embodiment) f = 392.36 Fno = 2.88 2ω = 6.31° R1 =117.835 D1 = 9.16 N1 = 1.4875 ν1 = 70.2 R2 = 171.288 D2 = 2.00 NGNL1 =1.6356 νGNL1 = 22.7 R3 = 198.370 (Aspherical D3 = 0.05 NGL1 = 1.5648νGL1 = 20.0 R4 = 174.689 Surface) D4 = 0.00 R5 = 174.689 D5 = 20.00 N2 =1.4875 ν2 = 70.2 R6 = −629.325 D6 = 9.39 R7 = 99.381 D7 = 15.59 N3 =1.4875 ν3 = 70.2 R8 = 441.881 D8 = 5.48 R9 = −727.900 D9 = 4.00 N4 =1.8340 ν4 = 37.2 R10 = 184.723 D10 = 20.80 R11 = 87.849 D11 = 9.00 N5 =1.4875 ν5 = 70.2 R12 = 251.334 D12 = 0.15 R13 = 54.908 D13 = 4.00 N6 =1.8052 ν6 = 25.4 R14 = 43.350 D14 = 37.71 R15 = 244.772 D15 = 2.80 N7 =1.6583 ν7 = 57.3 R16 = 63.310 D16 = 25.00 R17 = ∞ (Aperture Stop) D17 =2.27 R18 = −141.572 D18 = 4.00 N8 = 1.8467 ν8 = 23.8 R19 = −117.763 D19= 0.15 R20 = 65.966 D20 = 5.52 N9 = 1.5400 ν9 = 59.5 R21 = −105.637 D21= 3.00 N10 = 1.8340 ν10 = 37.2 R22 = 76.891 D22 = 28.89 R23 = 183.461D23 = 8.46 N11 = 1.6700 ν11 = 39.3 R24 = −44.576 D24 = 2.50 N12 = 1.5400ν12 = 59.5 R25 = 62.415 D25 = 8.57 R26 = 71.860 D26 = 6.00 N13 = 1.5927ν13 = 35.3 R27 = 710.477 Aspherical Coefficient k B C D E 3rd Surface1.8877E−01 6.4274E−09 −1.1579E−12 4.9144E−17 1.1708E−20

(Ninth Numerical Embodiment) f = 294.0 Fno = 4.14 2ω = 8.42° R1 =193.388 D1 = 8.76 N1 = 1.5212 ν1 = 67.0 R2 = −173.765 D2 = 1.20 NGNL1 =1.6356 νGNL1 = 22.7 R3 = −131.984 (Aspherical D3 = 0.05 NGL1 = 1.5648νGL1 = 20.0 R4 = −161.149 Surface) D4 = 0.15 R5 = 74.247 D5 = 6.64 N2 =1.4870 ν2 = 70.4 R6 = 176.418 D6 = 5.16 R7 = −257.193 D7 = 3.40 N3 =1.7641 ν3 = 27.9 R8 = 845.002 D8 = 0.15 R9 = 50.201 D9 = 8.33 N4 =1.4870 ν4 = 40.4 R10 = 138.171 D10 = 6.50 R11 = 45.368 D11 = 3.00 N5 =1.8490 ν5 = 26.7 R12 = 33.543 D12 = 11.75 R13 = ∞ (Aperture Stop) D13 =0.00 R14 = ∞ D14 = 4.00 R15 = 159.894 D15 = 3.17 N6 = 1.7294 ν6 = 27.0R16 = −216.482 D16 = 2.00 N7 = 1.8850 ν7 = 41.0 R17 = 81.708 D17 = 32.13R18 = 99.214 D18 = 1.60 N8 = 1.8500 ν8 = 23.0 R19 = 26.424 D19 = 7.15 N9= 1.5812 ν9 = 39.5 R20 = −50.918 D20 = 0.16 R21 = 95.554 D22 = 4.32 N10= 1.8600 ν10 = 26.4 R22 = −37.008 D23 = 1.50 N11 = 1.7800 ν11 = 50.0 R23= 26.014 D24 = 5.75 R24 = −24.230 D25 = 1.50 N12 = 1.6200 ν12 = 60.3 R25= −56.688 D26 = 2.93 R26 = 47.995 D27 = 7.97 N13 = 1.5450 ν13 = 46.5 R27= −28.966 D28 = 1.80 N14 = 1.8850 ν14 = 41.0 R28 = −63.496 AsphericalCoefficient k B C D E 5th Surface −4.36842E−01 2.38651E−08 3.19153E−135.47944E−15 4.24280E−19

(Tenth Numerical Embodiment) f = 294.0 Fno = 4.14 2ω = 8.42° R1 =117.454 D1 = 9.46 N1 = 1.7576 ν1 = 51.0 R2 = −286.088 D2 = 0.39 NGNL1 =1.7088 νGNL1 = 21.6 R3 = −247.645 D3 = 0.05 NGL1 = 1.5963 νGL1 = 13.9 R4= −308.068 D4 = 0.15 R5 = 112.842 D5 = 6.22 N2 = 1.4870 ν2 = 70.4 R6 =834.964 D6 = 5.13 R7 = −256.907 D7 = 3.40 N3 = 1.8564 ν3 = 25.1 R8 =203.308 D8 = 0.15 R9 = 50.401 D9 = 7.14 N4 = 1.4870 ν4 = 70.4 R10 =114.624 D10 = 8.24 R11 = 48.365 D11 = 3.00 N5 = 1.6192 ν5 = 60.3 R12 =33.797 D12 = 11.11 R13 = ∞ (Aperture Stop) D13 = 0.00 R14 = ∞ D14 = 4.00R15 = 165.324 D15 = 3.20 N6 = 1.7329 ν6 = 26.9 R16 = −177.058 D16 = 2.00N7 = 1.8850 ν7 = 41.0 R17 = 81.708 D17 = 33.37 R18 = 101.698 D18 = 1.60N8 = 1.8500 ν8 = 23.0 R19 = 27.778 D19 = 6.64 N9 = 1.6195 ν9 = 36.2 R20= −55.388 D20 = 0.40 R21 = 74.332 D22 = 4.06 N10 = 1.8615 ν10 = 27.0 R22= −51.973 D23 = 1.50 N11 = 1.7800 ν11 = 50.0 R23 = 25.549 D24 = 5.92 R24= −27.265 D25 = 1.50 N12 = 1.7800 ν12 = 50.0 R25 = −57.332 D26 = 2.68R26 = 46.891 D27 = 7.00 N13 = 1.5388 ν13 = 48.1 R27 = −30.034 D28 = 2.73N14 = 1.8850 ν14 = 41.0 R28 = −70.163

(Eleventh Numerical Embodiment) f = 294.0 Fno = 4.14 2ω = 8.42° R1 =155.141 D1 = 8.31 N1 = 1.5797 ν1 = 62.6 R2 = −266.200 D2 = 1.50 NGNL1 =1.6959 νGNL1 = 17.7 R3 = −167.163 D3 = 0.05 NGL1 = 1.5425 νGL1 = 29.0 R4= −220.744 D4 = 0.15 R5 = 92.229 D5 = 7.11 N2 = 1.5387 ν2 = 65.5 R6 =532.897 D6 = 3.14 R7 = −269.965 D7 = 3.40 N3 = 1.8654 ν3 = 28.7 R8 =130.581 D8 = 0.15 R9 = 84.739 D9 = 8.54 N4 = 1.4873 ν4 = 70.4 R10 =−562.348 D10 = 19.08 R11 = 41.082 D11 = 3.00 N5 = 1.4870 ν5 = 70.4 R12 =36.019 D12 = 10.63 R13 = ∞ (Aperture Stop) D13 = 0.00 R14 = ∞ D14 = 4.00R15 = 169.956 D15 = 3.76 N6 = 1.7498 ν6 = 26.2 R16 = −111.526 D16 = 2.00N7 = 1.8819 ν7 = 38.5 R17 = 81.708 D17 = 31.37 R18 = 93.664 D18 = 1.60N8 = 1.8500 ν8 = 23.0 R19 = 28.356 D19 = 6.58 N9 = 1.6279 ν9 = 42.0 R20= −61.505 D20 = 0.15 R21 = 78.718 D22 = 6.43 N10 = 1.8610 ν10 = 26.8 R22= −42.700 D23 = 1.50 N11 = 1.7568 ν11 = 51.0 R23 = 24.842 D24 = 5.87 R24= −27.135 D25 = 1.50 N12 = 1.5906 ν12 = 61.9 R25 = −86.343 D26 = 3.52R26 = 45.811 D27 = 9.72 N13 = 1.5202 ν13 = 53.8 R27 = −29.816 D28 = 3.00N14 = 1.8850 ν14 = 41.0 R28 = −67.113

(Twelfth Numerical Embodiment) f = 294.0 Fno = 4.14 2ω = 8.42° R1 =165.948 D1 = 9.02 N1 = 1.4870 ν1 = 70.4 R2 = −189.026 D2 = 0.15 R3 =107.153 D3 = 6.00 N2 = 1.4870 ν2 = 70.4 R4 = 379.005 D4 = 1.50 NGNL1 =1.5532 νGNL1 = 39.8 R5 = 27779.873 (Aspherical D5 = 0.05 NGL1 = 1.7127νGL1 = 13.8 R6 = 556.147 Surface) D6 = 5.47 R7 = −242.960 D7 = 3.40 N3 =1.8838 ν3 = 39.94 R8 = 503.260 D8 = 1.11 R9 = 83.132 D9 = 7.39 N4 =1.4870 ν4 = 70.4 R10 = 1008.384 D10 = 17.33 R11 = 51.173 D11 = 3.00 N5 =1.5115 ν5 = 64.0 R12 = 40.513 D12 = 10.12 R13 = ∞ (Aperture Stop) D13 =0.00 R14 = ∞ D14 = 4.00 R15 = 177.678 D15 = 4.00 N6 = 1.7652 ν6 = 25.6R16 = −105.297 D16 = 2.00 N7 = 1.8823 ν7 = 38.8 R17 = 81.708 D17 = 32.54R18 = 103.789 D18 = 1.60 N8 = 1.8564 ν8 = 25.1 R19 = 34.769 D19 = 6.04N9 = 1.6702 ν9 = 53.7 R20 = −79.264 D20 = 0.15 R21 = 49.645 D21 = 5.28N10 = 1.8585 ν10 = 26.3 R22 = −132.812 D22 = 1.50 N11 = 1.7276 ν11 =52.5 R23 = 23.745 D23 = 6.39 R24 = −41.576 D24 = 1.50 N12 = 1.6958 ν12 =54.4 R25 = 342.785 D25 = 4.04 R26 = 47.170 D26 = 7.53 N13 = 1.5269 ν13 =51.6 R27 = −30.301 D27 = 1.80 N14 = 1.8850 ν14 = 41.0 R28 = −67.490Aspherical Coefficient k B C D E 7th Surface 1.46158E+05 1.69205E−09−3.32770E−12 1.16835E−15 −5.92857E−19

(Thirteenth Numerical Embodiment) f = 294.0 Fno = 4.14 2ω = 8.42° R1 =157.370 D1 = 8.97 N1 = 1.5163 ν1 = 64.1 R2 = −204.567 D2 = 0.76 NGNL1 =1.6356 νGNL1 = 22.7 R3 = −168.921 D3 = 0.15 R4 = 96.414 D4 = 8.62 N2 =1.5638 ν2 = 60.7 R5 = −643.669 D5 = 0.05 NGL1 = 1.5425 νGL1 = 29.1 R6 =1526.834 D6 = 2.80 R7 = −228.046 D7 = 3.40 N3 = 1.8340 ν3 = 37.2 R8 =129.968 D8 = 0.73 R9 = 72.569 D9 = 8.93 N4 = 1.4875 ν4 = 70.2 R10 =5162.619 D10 = 13.48 R11 = 43.936 D11 = 3.50 N5 = 1.8052 ν5 = 25.4 R12 =37.942 D12 = 10.71 R13 = ∞ (Aperture Stop) D13 = 4.00 R14 = 139.290 D14= 4.00 N6 = 1.7215 ν6 = 29.2 R15 = −133.808 D15 = 2.00 N7 = 1.8830 ν7 =40.8 R16 = 81.708 D16 = 29.31 R17 = 133.715 D17 = 1.80 N8 = 1.8467 ν8 =23.8 R18 = 27.935 D18 = 8.13 N9 = 1.6668 ν9 = 33.1 R19 = −60.022 D19 =0.15 R20 = 90.843 D20 = 6.00 N10 = 1.8340 ν10 = 37.2 R21 = −39.347 D21 =2.30 N11 = 1.7725 ν11 = 49.6 R22 = 26.618 D22 = 5.82 R23 = −26.518 D23 =1.50 N12 = 1.4875 ν12 = 70.2 R24 = −107.094 D24 = 2.58 R25 = 50.997 D25= 9.00 N13 = 1.5481 ν13 = 45.8 R26 = −31.115 D26 = 3.00 N14 = 1.8830 ν14= 40.8 R27 = −64.669

TABLE 4 Eighth Embodiment Ninth Embodiment Tenth Embodiment First SecondFirst Second Second Optical Optical Optical Optical First OpticalOptical Element GNL1 Element GL1 Element GNL1 Element GL1 Element GNL1Element GL1 UV- 14.2% ITO - UV- 14.2% ITO - 20% TiO2 - 20% ITO -Conditional curable UV-curable curable UV-curable UV-curable UV-curableExpression resin 1 resin 2 resin 1 resin 2 resin 2 resin 2 Nd 1.63561.5648 1.6356 1.5648 1.7088 1.5963 Ng 1.6753 1.5941 1.6753 1.5941 1.75991.6383 NC 1.6281 1.5544 1.6281 1.5544 1.7003 1.5804 NF 1.6560 1.58261.6560 1.5826 1.7331 1.6234 13, 14 νd 22.73 20.03 22.73 20.03 21.6313.86 θgd 1.4220 1.0517 1.4220 1.0517 1.5594 0.9761 θgF 0.6895 0.41970.6895 0.4194 0.8170 0.3459 11, 12 Δθgd 0.0826 −0.2996 0.0826 −0.29960.2152 −0.4049  9, 10 ΔθgF 0.0652 −0.2147 0.0652 −0.2147 0.1888 −0.313015 φ 0.000521 −0.000386 0.001171 −0.000774 0.000386 −0.000472  8 Lt/ft0.764 0.669 0.669 Eleven Embodiment Twelfth Embodiment ThirteenthEmbodiment Second First Second First Optical Optical First OpticalSecond Optical Optical Optical Element GNL1 Element GL1 Element GNL1Element GL1 Element GNL1 Element GL1 N- 5% ITO - 3% TiO2 - 10% ITO - N-UV- 5% ITO - Conditional polyvinyl UV-curable UV-curable polyvinylcurable UV-curable Expression carbazole resin 2 resin 2 carbazole resin1 resin 2 Nd 1.6959 1.5425 1.5532 1.7127 1.6356 1.5425 Ng 1.7516 1.56301.5725 1.7772 1.6753 1.5630 NC 1.6853 1.5362 1.5494 1.6969 1.6281 1.5362NF 1.7246 1.5549 1.5633 1.7483 1.6560 1.5549 13, 14 νd 17.68 29.05 39.8113.85 22.73 29.05 θgd 1.4155 1.0963 1.3852 1.2527 1.4220 1.0963 θgF0.6856 0.4346 0.6645 0.5604 0.6895 0.4346 11, 12 Δθgd 0.0533 −0.21780.1063 −0.1283 0.0826 −0.2178  9, 10 ΔθgF 0.0424 −0.1688 0.0898 −0.09860.0652 −0.1688 15 φ 0.001558 −0.000787 0.001440 −0.001256 0.000661−0.001198  8 Lt/ft 0.720 0.748 0.737

TABLE 5 UV Curable Resin 2 ITO TiO2 Nd 1.5241 1.8571 2.3038 Ng 1.53711.9924 2.4568 NC 1.5212 1.7979 2.2803 NF 1.5313 1.9487 2.3745 νd 51.555.69 13.84 θgd 1.2695 0.8976 1.6241 θgF 0.5631 0.2901 0.8731

TABLE 6 Conditional Eighth Expression Embodiment Ninth Embodiment TenthEmbodiment ΔθgF1 × φ1/νd1 1.4955E−06 3.3613E−06 3.3697E−06 ΔθgF2 ×φ2/νd2 4.1376E−06 8.2967E−06 1.0657E−05 16 (ΔθgF1 × φ1/νd1)/(ΔθgF2 ×φ2/νd2) 3.6144E−01 4.0513E−01 3.1618E−01 Conditional Eleven TwelfthThirteenth Expression Embodiment Embodiment Embodiment ΔθgF1 × φ1/νd13.7344E−06 3.2472E−06 1.8974E−06 ΔθgF2 × φ2/νd2 4.5726E−06 8.9444E−066.9605E−06 16 (ΔθgF1 × φ1/νd1)/(ΔθgF2 × φ2/νd2) 8.1669E−01 3.6304E−012.7259E−01

An optical system according to an exemplary embodiment of the presentinvention is described below. The intersecting point of a light axis Laand a paraxial chief ray R is defined as “P”. This optical system is aretrofocus optical system that is configured so that the maximum heightof the paraxial marginal ray from the light axis when the paraxialmarginal ray passes through the lens surface on the enlargement side ofthe point P is less than that on the reduction side relative to thepoint P. That is, the optical system has a focal length shorter than thetotal lens length thereof (the distance between the first lens surfaceand the image plane).

According to the present exemplary embodiment, the optical system OLincludes a first optical element and a second optical element on atleast one of the enlargement side and the reduction side relative to thepoint P. Each of the first optical element and the second opticalelement has a refractive light incident surface and a refractive lightemergent surface and is made of a solid material.

Each of the first and second optical elements is a refractive opticalelement (hereinafter simply referred to as an “optical element”) havinga refractive power that satisfies the following conditions.

As used herein, the term “solid material” of the refractive opticalelement refers to a material that is solid in a use environment of theoptical system. Accordingly, the material may be in any state before theoptical system is in use (e.g., during a fabrication period). Forexample, even when the material is liquid during the fabrication period,the material is referred to as a “solid material” if the liquid materialis cured into a solid material.

FIG. 38 is a schematic illustration of a paraxial refractive powerarrangement for illustrating the optical function of the optical systemaccording to the present embodiment. In FIG. 38, an object is located onthe left side (the enlargement side), and an image plane is located onthe right side (the reduction side).

As shown in FIG. 38, an optical system OL is of a retrofocus type havingthe total lens length (the distance between the first lens surface andthe image plane) that is greater than the focal length. The telephotooptical system OL includes a front lens group Gn having a negativerefractive power and a rear lens group Gp having a positive refractivepower. The rear lens group Gp includes a first refractive opticalelement (a first optical element) GNL1 and a second refractive opticalelement (a second optical element) GL1 composed of a material thatsatisfies the following conditional expressions (18) to (27).

For simplicity, all of the lenses included in the front lens group Gnand the rear lens group Gp are thin single lenses. These lenses aredisposed along a light axis La in the front lens group Gn and the rearlens group Gp so that the distances therebetween are zero. In addition,each of the first optical element GNL1 and the second optical element GLis a thin single lens. The first optical element GNL1 and the secondoptical element GL1 are disposed along the light axis La in the rearlens group Gp so that the distance therebetween is zero.

Although, in FIG. 38, the first and second optical element GNL1 and GL1are disposed in the rear lens group Gp, the first and second opticalelements GNL1 and GL1 may be disposed in the front lens group Gn ifconditional expressions (18) to (27) are satisfied.

A paraxial marginal ray Q is a paraxial ray that, when the focal lengthof the entire optical system is normalized to “1”, travels parallel tothe light axis of the optical system at a height of “1” from the lightaxis and is made incident on the optical system.

It is assumed that an object is disposed on the left side of the opticalsystem, and a light ray made incident on the optical system from theobject side travels from the left to the right. A paraxial chief ray Ris a paraxial ray that, when the focal length of the entire opticalsystem is normalized to “1”, passes through an intersection between theentrance pupil and the light axis of the optical system among light raysmade incident on the optical system at an angle of −45° with respect tothe light axis. The incident angle of a ray is positive if the ray ismeasured from the light axis in a clockwise direction, while theincident angle is negative if the ray is measured from the light axis ina counterclockwise direction. The intersecting point of the light axisLa and a paraxial chief ray R is defined as “P”. The image plane isdenoted as “IP”.

As shown in FIG. 38, in the optical system OL, a maximum height h_(Gn)of the paraxial marginal ray Q from the light axis La when the paraxialmarginal ray Q passes through the lens surface on the enlargement sideis smaller than a maximum height h_(Gp) of the paraxial marginal ray Qfrom the light axis La when the paraxial marginal ray Q passes throughthe lens surface on the reduction side. That is, H_(Gn) and H_(Gp)represent the heights of the paraxial chief ray R from the light axis Lawhen the paraxial chief ray R is made incident on the front lens groupGn and the rear lens group Gp, respectively.

The features of the optical system OL according to the present exemplaryembodiment are described next.

Let ft denote the focal length of the entire optical system, and Ltdenote the total lens length of the optical system.

The optical system OL includes a first optical element GNL1 and a secondoptical element GL1 on at least one of the enlargement side and thereduction side relative to the point P. Each of the first opticalelement GNL1 and the second optical element GNL2 has a refractive lightincident surface and a refractive light emergent surface and is made ofa solid material.

Let ΔθgF1 and ΔθgF2 denote the anomalous partial dispersion values ofthe first optical element GNL1 and the second optical element GL1 forthe Fraunhofer g-line and F-line, respectively.

Let φ1 and φ2 denote the refractive powers of the first optical elementGNL1 and the second optical element GL1 when the incident and emergentsurfaces of the first optical element GNL1 and the second opticalelement GL1 are in contact with air.

Let Δθgd1 and Δθgd2 denote the anomalous partial dispersion values ofthe materials of the first optical element GNL1 and the second opticalelement GL1 for the Fraunhofer g-line and d-line, respectively.

Let νd1 and νd2 denote the Abbe numbers of the solid materials of thefirst optical element GNL1 and the second optical element GL1,respectively.

Then, at least one of the following conditions is satisfied:

2<Lt/ft<15  (17)

ΔθgF1>0.0272  (18)

ΔθgF2<−0.0278  (19)

Δθgd1>0.038  (20)

Δθgd2<−0.037  (21)

νd1<60  (22)

νd2<60  (23)

φ1×φ2<0  (24)

Let φ1a and φ2a denote the refractive powers of the first opticalelement and the second optical element disposed on the reduction siderelative to the point P, respectively. Let νd1a and νd2a denote the Abbenumbers of the materials of the first optical element and the secondoptical element, respectively. Let ΔθgF1a and ΔθgF2a denote theanomalous partial dispersion values of the first optical element and thesecond optical element for the g-line and F-line, respectively.

Then, at least one of the following two conditional expressions issatisfied:

(φ1a×ΔθgF1a/νd1a)/(φ2a×ΔθgF2a/νd2a)>0.8  (25)

φ1a>0 and φ2a<0  (26)

Let φ1b and φ2b denote the refractive powers of the first opticalelement and the second optical element disposed on the enlargement siderelative to the point P, respectively. Then, the following conditionalexpression is satisfied:

φ1b<0 and φ2b>0  (27)

For the optical element used in the optical system according to thepresent exemplary embodiment, the Abbe number νd, the relative partialdispersion θgd of the solid material for the Fraunhofer g-line andd-line, and the relative partial dispersion θgF of the solid materialfor the Fraunhofer g-line and F-line are defined as follows:

νd=(Nd−1)/(NF−NC)

θgd=(Ng−Nd)/(NF−NC)

θgF=(Ng−NF)/(NF−NC)

where Ng, NF, Nd, and NC denote the indices of refraction of the solidmaterial for the Fraunhofer g-line (wavelength=435.8 nm), the FraunhoferF-line (wavelength=486.1 nm), the Fraunhofer d-line (wavelength=587.6nm), and the Fraunhofer C-line (wavelength=656.3 nm), respectively.

In general, the relative partial dispersions θgd and θgF of the solidmaterial used for a lens system are approximated as follows:

θgd=−1.687×10⁻⁷ νd ³+5.702×10⁻⁵ νd ²−6.603×10⁻³ νd+1.462

θgF=−1.665×10⁻⁷ νd ³+5.213×10⁻⁵ νd ²−5.656×10⁻³ νd+0.7278

Here, the anomalous partial dispersion values Δθgd and ΔθgF for theg-line and d-line and for the g-line and F-line, respectively, areexpressed as follows:

Δθgd=θgd−(−1.687×10⁻⁷ νd ³+5.702×10⁻⁵ νd ²−6.603×10⁻³ νd+1.462)

ΔθgF=θgF−(−1.665×10⁻⁷ νd ³+5.213×10⁻⁵ νd ²−5.656×10⁻³ νd+0.7278)

According to the present exemplary embodiment, the optical system OLincludes at least one first refractive optical element GNL1 that iscomposed of a solid material having high dispersion and high relativepartial dispersion and at least one second refractive optical elementGL1 that is composed of a solid material having high dispersion and lowrelative partial dispersion.

As used herein, the term “refractive optical element” refers to anoptical element, such as a refractive lens, that produces refractivepower using a refracting effect. Thus, a diffractive optical elementthat produces refractive power using a diffracting effect is notincluded in the category of the term “refractive optical element”.

The above-described conditional expressions are technically describednext.

The optical system of the present exemplary embodiment is one ofretrofocus optical systems that satisfy conditional expression (17). Inthe optical systems that satisfy conditional expression (17), bysatisfying at least one of conditional expressions (18) to (27), anadvantage corresponding to the conditional expression can be effectivelyobtained.

According to the present exemplary embodiment, by employing at least onefirst optical element GNL1 composed of a solid material that satisfiesconditional expression (18) and at least one second optical element GL1composed of a solid material that satisfies conditional expression (19),chromatic aberration of the optical system in the range of thewavelength of visible light can be sufficiently corrected.

By employing the first optical element GNL1 and the second opticalelement GL1 that satisfy conditional expressions (20) and (21),chromatic aberration of the optical system in the range of a shortwavelength to a medium wavelength can be easily and sufficientlycorrected. If the optical system satisfies all the conditionalexpressions (18) to (21), chromatic aberration of the optical system ina wide range of a short wavelength to a long wavelength can be furthersufficiently corrected.

By employing solid materials that satisfy conditional expressions (22)and (23) for the first and second optical elements GNL1 and GL1,chromatic aberration of the optical system can be easily corrected.

By configuring the refractive powers of the first optical element GNL1and the second optical element GL1 so that conditional expression (24)is satisfied, chromatic aberration of the optical system in a widewavelength range can be sufficiently corrected.

In addition, in the case where the first optical element GNL1 and thesecond optical element GL1 are disposed on the reduction side relativeto the point P, it is desirable that the refractive powers and thematerials of the first optical element GNL1 and the second opticalelement GL1 satisfy at least one of conditional expressions (25) and(26).

In contrast, in the case where the first optical element GNL1 and thesecond optical element GL1 are disposed on the enlargement side relativeto the point P, it is desirable that conditional expression (27) isfurther satisfied.

In this way, chromatic aberration can be easily and sufficientlycorrected by the optical system of a retrofocus type according to thepresent exemplary embodiment.

In the present exemplary embodiment, when the first optical element GNL1and the second optical element GL1 are provided in the optical system,it is desirable that both the first optical element GNL1 and the secondoptical element GL1 are disposed on each of the enlargement side and thereduction side relative to the point P at which the light axis Laintersects the paraxial chief ray R. Thus, chromatic aberration of theoptical system can be further sufficiently corrected.

Examples of the solid material (optical material) that satisfiesconditional expression (18) include a variety of resins.

Among the variety of resins, a UV-curable resin (Nd=1.63, νd=22.7, andθgF=0.69) and N-polyvinyl carbazole (Nd=1.696, νd=17.7, and θgF=0.69)are optical materials that satisfy conditional expression (18). However,in addition to these materials, any solid material that satisfiesconditional expression (18) can be employed.

In addition, an optical material having a characteristic that isdifferent from that of a widely used glass material can be used.Examples of such an optical material include a mixture of a syntheticresin and inorganic oxide nanoparticles dispersed therein. Examples ofthe inorganic oxide nanoparticles include TiO₂ particles (Nd=2.304 andνd=13.8), Nb₂O₅ particles (Nd=2.367 and νd=14.0), ITO particles(Nd=1.8571 and νd=5.69), CrO₃ particles (Nd=2.2178 and νd=13.4), andBaTiO₃ particles (Nd=2.4362 and νd=11.3).

Among these types of inorganic oxide, by dispersing TiO₂ particles(Nd=2.304, νd=13.8, and θgF=0.87) in a synthetic resin in an appropriatevolume ratio, an optical material that satisfies conditional expression(18) can be obtained.

In addition, by dispersing ITO fine particles (Nd=1.8571, νd=5.69, andθgF=0.873) in a synthetic resin in an appropriate volume ratio, anoptical material that satisfies conditional expression (19) can beobtained. However, in addition to these materials, any solid materialsthat satisfy conditional expressions (18) and (19) can be employed.

In the exemplary embodiments, by using an optical material having arelative partial dispersion higher than that of a widely used opticalmaterial and an optical material having a relative partial dispersionlower than that of a widely used optical material, the chromaticaberration is sufficiently corrected.

In the wavelength-dependent characteristic of the index of refraction(dispersion characteristic) of an optical material, the Abbe numberrepresents the slope of the dispersion characteristic curve, and therelative partial dispersion represents the curvature of the dispersioncharacteristic curve.

In general, the index of refraction of an optical material in ashort-wavelength range is higher than that in a long-wavelength range.At that time, the Abbe number and the relative partial dispersion arepositive.

Accordingly, the dispersion characteristic curve is downwardly convex. Achange in the index of refraction relative to a change in the wavelengthincreases towards a short-wavelength range. For example, refractiveindex characteristics with respect to a wavelength for S-BSL7 (Nd=1.516and νd=64.1) and S-TIH53 (Nd=1.847 and νd=23.8) available from OHARAcorporation are shown in FIG. 41.

In addition, a high-dispersion optical material having a smaller Abbenumber tends to have a higher relative partial dispersion θgF for g-lineand F-line and a higher relative partial dispersion θgd for g-line andd-line.

In widely used optical materials, the relative partial dispersionsubstantially linearly changes with respect to the Abbe number. However,an optical material having an anomalous partial dispersion changesdifferently from the linear change. A typical example of such ananomalous partial dispersion material is fluorite.

The wavelength-dependent characteristic curve of a chromatic aberrationcoefficient of an optical material having a high relative partialdispersion has a large curvature in a short-wavelength range, comparedwith that of a widely used optical material.

When the refractive power of the lens surface of an optical materialhaving a high relative partial dispersion is changed in order to controlthe chromatic aberration, the slope of the entire wavelength-dependentcharacteristic curve of a chromatic aberration coefficient changes suchthat the entire wavelength-dependent characteristic curve rotates abouta point of a reference design wavelength. In particular, the change issignificant in a short-wavelength range for an optical material having ahigh relative partial dispersion. As a result, the slope of the entirewavelength-dependent characteristic curve is changed while significantlychanging the curvature in the short-wavelength range.

By using this property, the curvature of the wavelength-dependentcharacteristic curve of a chromatic aberration coefficient in theshort-wavelength range can be canceled. However, it is difficult tocorrect the remaining slope of the wavelength-dependent characteristiccurve of a chromatic aberration coefficient at the same time. Inaddition, the correction of the curvature in the short-wavelength rangerelatively increases chromatic aberration in a long-wavelength range. Toprevent the increase in chromatic aberration in a long-wavelength range,the refractive power of an appropriate one of the glass surfaces of theoptical system needs to be changed. However, this is not suitable forcorrecting a variety of aberrations other than chromatic aberration.

In contrast, the wavelength-dependent characteristic curve of achromatic aberration coefficient of an optical material having a lowrelative partial dispersion has a small curvature in a short-wavelengthrange. Accordingly, the chromatic aberration coefficient linearlychanges with a change in wavelength, compared with that of a widely usedoptical material. When the refractive power of the lens surface of anoptical material having a low relative partial dispersion is changed inorder to control the chromatic aberration, the slope of the entirewavelength-dependent characteristic curve of a chromatic aberrationcoefficient changes such that the entire wavelength-dependentcharacteristic curve rotates about a point of a reference designwavelength while relatively retaining linearity with respect to thewavelength. In this way, the slope of the wavelength-dependentcharacteristic curve of a chromatic aberration coefficient can becorrected.

Accordingly, by employing an optical material having a high relativepartial dispersion in addition to an optical material having a lowrelative partial dispersion, the curvature of the wavelength-dependentcharacteristic curve of a chromatic aberration coefficient in ashort-wavelength range and the slope of the entire wavelength-dependentcharacteristic curve can be corrected at the same time. That is, thechromatic aberration of the optical system can be sufficiently correctedin a wide wavelength range of the g-line to C-line.

Such correction of chromatic aberration of an optical system isdescribed next with reference to an optical system including arefractive optical system portion GNL using an optical material having ahigh relative partial dispersion, a refractive optical system portion GLusing an optical material having a low relative partial dispersion, anda refractive optical system portion G using a widely used opticalmaterial having a normal relative partial dispersion.

Chromatic aberration of the refractive optical system portion G iscorrected to some extent first. Then, a relatively high-dispersionoptical material is selected for a negative lens included in therefractive optical system portion G. The slope of the entirewavelength-dependent characteristic curve of a chromatic aberrationcoefficient of the refractive optical system portion G is changed whilethe portion in a short-wavelength range is significantly curved from theoriginal shape.

At that time, an appropriate refractive power is provided to therefractive optical system portion GNL, and a relatively high-dispersionoptical material is selected for a positive lens included in therefractive optical system portion G. However, in the case where therefractive optical system portion GNL is composed of a widely usedoptical material having a uniform relative partial dispersion withrespect to an Abbe number, the refractive optical system portion GNL ispartially responsible equally for a curvature component and a slopecomponent of the wavelength-dependent characteristic curve of achromatic aberration coefficient of the refractive optical systemportion G. Therefore, the curvature component and the slope componentcannot be canceled at the same time.

In contrast, in the case where the refractive optical system portion GNLis composed of an optical material having a relative partial dispersionhigher than that of a widely used optical material, the refractiveoptical system portion GNL is relatively largely responsible for theslope component of the entire wavelength-dependent characteristic curveof a chromatic aberration coefficient of the main refractive opticalsystem portion G. Therefore, the curvature component can be mainlycanceled. As a result, the slope of the entire wavelength-dependentcharacteristic curve of a chromatic aberration coefficient can bechanged while increasing linearity from the original shape.

At that time, by further providing the refractive optical system portionGL with an appropriate refractive power with a plus/minus sign oppositeto that of the refractive optical system portion GNL, the slope of theentire wavelength-dependent characteristic curve of a chromaticaberration coefficient of the refractive optical system portion G can becorrected.

However, if the refractive optical system portion GL is composed of awidely used optical material, the refractive optical system portion GLhas a characteristic in which the wavelength-dependent characteristiccurve of a chromatic aberration coefficient is relatively largely convexin a direction opposite to that corresponding to thewavelength-dependent characteristic curve of the refractive opticalsystem portion G.

Accordingly, although the slope component of the entirewavelength-dependent characteristic curve of a chromatic aberrationcoefficient can be canceled, a curvature component that increases thechromatic aberration occurs. At that time, to correct the curvaturecomponent of the entire wavelength-dependent characteristic curve of achromatic aberration coefficient, the refractive power of the refractiveoptical system portion GNL composed of a material having a high relativepartial dispersion needs to be further changed. However, if therefractive power is further changed, the thickness of the lens in thelight axis direction disadvantageously increases.

In contrast, in the case where the refractive optical system portion GLis composed of an optical material having a low relative partialdispersion, the linearity of the wavelength-dependent characteristiccurve of a chromatic aberration coefficient of the refractive opticalsystem portion GL is relatively increased. That is, by changing therefractive power of the refractive optical system portion GL in order tocorrect the chromatic aberration, the slope of the wavelength-dependentcharacteristic curve of a chromatic aberration coefficient can bechanged so that the wavelength-dependent characteristic curve rotatesabout the point of the design reference wavelength while substantiallymaintaining linearity. Accordingly, the chromatic aberration can besufficiently corrected.

As described above, by using the refractive optical system portion GNLand the refractive optical system portion GL for the main refractiveoptical system portion G, the slope component and the curvaturecomponent of the wavelength-dependent characteristic curve of achromatic aberration coefficient can be relatively easily corrected atthe same time.

FIG. 39 illustrates a relationship between the axial chromaticaberration coefficient L and a wavelength in a retrofocus opticalsystem. According to the present exemplary embodiment, chromaticaberration in the entire wavelength range of visible light can becorrected. This is described in more detail below.

In FIG. 39, the term “before correction” indicates thewavelength-dependent characteristic curve of a chromatic aberrationcoefficient before the refractive optical system portions GNL and GL areemployed.

An appropriate refractive power is provided to the refractive opticalsystem portion GNL of such an optical system so that the curvature ofthe wavelength-dependent characteristic curve of a chromatic aberrationcoefficient in a short-wavelength range.

Furthermore, an appropriate refractive power is provided to therefractive optical element GL of the optical system so that the slopecomponent of the wavelength-dependent characteristic curve of achromatic aberration coefficient of the refractive optical systemportion GNL is corrected. At that time, the product of the refractivepowers of the refractive optical system portion GNL and the refractivepower of the refractive optical system portion GL becomes negative. As aresult, according to the wavelength-dependent characteristic curve of achromatic aberration coefficient after the correction, the curvaturecomponent in the short-wavelength range can be corrected withoutdeteriorating the chromatic aberration characteristic in thelong-wavelength range. Thus, the chromatic aberration can be correctedin the entire wavelength range of visible light.

To sufficiently correct chromatic aberration by using one of therefractive optical system portion GNL and the refractive optical systemportion GL, the refractive power of a lens surface of one of therefractive optical system portion GNL and the refractive optical systemportion GL and the refractive power of a lens surface of the refractiveoptical system portion G need to be increased.

That is, by employing the refractive optical system portions GNL and GL,the refractive power of each of the refractive optical system portionGNL and the refractive optical system portion GL can be relativelyreduced. As a result, the thickness of the solid material in the lightaxis direction can be reduced.

Furthermore, by employing the refractive optical system portions GNL andGL, the chromatic aberration can be reduced without significantlychanging the refractive power of the refractive optical system portionG. Accordingly, a variety of aberrations other than the chromaticaberration can be maintained unchanged.

At that time, in order to independently correct chromatic aberration,the refractive optical system portion GNL and the refractive opticalsystem portion GL can have a small Abbe number, that is, can be composedof a high-dispersion optical material. Furthermore, in retrofocusoptical systems, at least one refractive optical system portion GNL andat least one refractive optical system portion GL can be disposed on thereduction side relative to the point P at which the paraxial chief rayintersects the light axis. This is described in detail next withreference to an axial chromatic aberration coefficient and a chromaticaberration coefficient of magnification of a lens surface.

Let ΔΨ denote a change in refractive power of a surface of a refractivelens, and ν denote the Abbe number. Let h and H denote the heights ofthe paraxial marginal ray and the paraxial chief ray from the light axiswhen the paraxial marginal ray and the paraxial chief ray pass throughthe surface of the refractive lens, respectively. Then, a change ΔL inthe axial chromatic aberration coefficient and a change ΔT in achromatic aberration coefficient of magnification can be expressed asfollows:

ΔL=h ²·ΔΨ/ν  (a)

ΔT=h·H·ΔΨ/ν  (b)

As can be seen from equations (a) and (b), the changes in theseaberration coefficients with respect to a change in the refractive powerof the lens surface increase as the absolute value of the Abbe numberdecreases (i.e., as the dispersion increases). Accordingly, by using ahigh-dispersion material having a small absolute value of the Abbenumber, the change amount of the refractive power that is required forobtaining a desired chromatic aberration can be reduced.

According to an aberration theory, this allows the chromatic aberrationto be controlled without significantly affecting the sphericalaberration, coma aberration, and astigmatism aberration. Thus, thechromatic aberration can be highly independently controlled.

In contrast, if a low-dispersion material is employed, the change amountof the refractive power that is required for obtaining a desiredchromatic aberration is increased. With the increase in the changeamount of the refractive power, a variety of aberrations, such asspherical aberration, significantly change. Thus, the chromaticaberration cannot be independently controlled. Therefore, in order tocorrect aberrations, it is important that, among the lenses of theoptical system, at least one of the surfaces of the lenses is a surfaceof a refractive lens made of a high-dispersion material.

In addition, equations (a) and (b) indicate that the changes in theaxial chromatic aberration coefficient and the chromatic aberrationcoefficient of magnification are determined by the values of the heightsh and H. Using this result, the optimal arrangement of the refractiveoptical system portion GNL and the refractive optical system portion GLin the optical system is described next.

To sufficiently correct chromatic aberration, the slope component andthe curvature component of the wavelength-dependent characteristic curveof a chromatic aberration coefficient need to be corrected at the sametime. However, if the refractive power change ΔΨ is decreased,sufficient correction of the chromatic aberration cannot be achieved.Conversely, if the refractive power change ΔΨ is increased, thethickness of an optical element (i.e., a lens) is increased.

In general, since the transmittance of the optical material of therefractive optical system portion GNL and the refractive optical systemportion GL having an anomalous partial dispersion characteristic is low,the thickness of a lens composed of the optical material needs to berelatively reduced. In addition, as the thickness decreases, a change inthe optical performance with a change in the surrounding environmentdecreases. Accordingly, the resistance to the surrounding environmentincreases. Thus, molding of the lens is facilitated.

That is, in order to reduce the thicknesses of the refractive opticalsystem portion GNL and the refractive optical system portion GL andsufficiently correct the chromatic aberration, the correction amounts ofthe slope component and the curvature component of thewavelength-dependent characteristic curve of a chromatic aberrationcoefficient can be appropriately controlled. According to equations (a)and (b), the correction amounts are determined by the heights h and H.Accordingly, the correction amounts change in accordance with thepositions of the refractive optical system portions GNL and GL in theoptical system. That is, in order to sufficiently correct the chromaticaberration and reduce the change amounts of the refractive powers of therefractive optical system portions GNL and GL, it is important to selectthe appropriate positions at which the refractive optical systemportions GNL and GL are disposed.

The appropriate positions of the refractive optical system portions GNLand GL at which the chromatic aberration is sufficiently corrected andthe change amounts of the refractive powers are reduced depend on theaberration structure of the optical system. In addition, the aberrationstructure varies in accordance with the type of optical system.

The sign (positive or negative) correlation between ΔL and ΔT isdiscussed next. The sign of ΔL/AT is determined by the sign of theheight h and the sign of the height H. In general, the height h isalways positive. The sign of the height H is negative on the enlargementside relative to the point P, while the sign of the height H is positiveon the reduction side relative to the point P.

In retrofocus optical systems, axial chromatic aberration and chromaticaberration of magnification can be easily corrected at the same timewhen ΔL/AT is positive.

Therefore, in the retrofocus optical system according to the presentembodiment, the refractive optical system portions GNL and GL can bedisposed on the reduction side relative to the point P. In this way,axial chromatic aberration and chromatic aberration of magnification canbe sufficiently corrected at the same time.

In addition, by letting the optical performance of the refractiveoptical system portions GNL and GL satisfy conditional expression (25),the curvature component and the slope component of thewavelength-dependent characteristic curve of a chromatic aberrationcoefficient can be sufficiently corrected, and the thicknesses of therefractive optical system portions GNL and GL can be reduced.

At that time, in order to cancel the curvature component and the slopecomponent of the wavelength-dependent characteristic curve of achromatic aberration coefficient, the product (φ1×φ2) of the refractivepower of the refractive optical system portion GNL (φ1) and therefractive power of the refractive optical system portion GL (φ2) can benegative, as indicated by conditional expression (24). This is due tothe wavelength-dependent characteristic of chromatic aberration of theretrofocus optical system.

In general, when a lens group is moved in order to perform zooming andfocusing and control the position of the image, the states of a ray madeincident on the lens groups change, and therefore, aberrations occurringin the lens groups change. Accordingly, in order to sufficiently correctthe aberrations of the optical system in all the use cases, aberrationcoefficients that simultaneously change in all the use cases need to bedetermined for each of the lens groups. By disposing the refractiveoptical system portions GNL and GL in the same lens group, desiredaberration values can be easily obtained.

In addition, if the thicknesses of the refractive optical systemportions GNL and GL are reduced, a change in the characteristic due tothe surrounding environment is reduced. Furthermore, by satisfyingconditional expression (24), the changes in the characteristics of therefractive optical system portions GNL and GL cancel each other out.Therefore, the resistance to the surrounding environment can beincreased.

A variety of aberrations including chromatic aberration are corrected bythe refractive optical system portions GNL and GL in cooperation with awidely used optical material. Accordingly, the characteristics of therelative partial dispersions of the refractive optical system portionsGNL and GL need to be different from that of the widely used opticalmaterial in order to correct the aberrations. However, a stronganomalous partial dispersion should be avoided.

When a lens made of an optical material having a characteristicsignificantly different from that of a widely used optical material isemployed, the curvature of the wavelength-dependent characteristic curveof a chromatic aberration coefficient of the lens surface isparticularly large. To correct the large curvature component, therefractive powers of other lenses need to be increased. This givessignificant impact on the spherical aberration, the coma aberration, andthe astigmatism aberration. Thus, it is difficult to correct theseaberrations.

That is, the material of the refractive optical system portion GNL needsto be an optical material having a relative partial dispersion higherthan that of a widely used optical material, but not having a relativepartial dispersion significantly different from that of a widely usedoptical material.

In the retrofocus optical system according to the present exemplaryembodiment, to obtain further sufficient correction of chromaticaberration, the range defined by conditional expression (17) can beredefined as follows:

3<Lt/ft<12  (17a)

In addition, to obtain further sufficient correction of chromaticaberration, the range of the anomalous partial dispersion value ΔθgF1 inconditional expression (18) relating to the first optical element GNL1can be redefined as follows:

0.0272<ΔθgF1<0.2832  (18a)

To obtain still further sufficient correction of chromatic aberration,the range of the anomalous partial dispersion value ΔθgF1 defined byconditional expression (18a) can be redefined as follows:

0.0342<ΔθgF1<0.2832  (18b)

To obtain further sufficient correction of chromatic aberration, therange of the anomalous partial dispersion value ΔθgF2 defined byconditional expression (19) relating to the second optical element GL1can be redefined as follows:

−0.4278<ΔθgF2<−0.0528  (19a)

To obtain still further sufficient correction of chromatic aberration,the range of the anomalous partial dispersion value ΔθgF2 defined byconditional expression (19a) can be redefined as follows:

−0.4278<ΔθgF2<−0.0778  (19b)

To obtain further sufficient correction of chromatic aberration, therange of the anomalous partial dispersion value Δθgd1 defined byconditional expression (11) relating to the first optical element GNL1can be redefined as follows:

0.038<Δθgd1<0.347  (20a)

To obtain still further sufficient correction of chromatic aberration,the range of the anomalous partial dispersion value Δθgd1 defined byconditional expression (20a) can be redefined as follows:

0.051<Δθgd1<0.347  (20b)

To obtain further sufficient correction of chromatic aberration, therange of the anomalous partial dispersion value Δθgd2 defined byconditional expression (21) relating to the second optical element GL1can be redefined as follows:

−0.5620<Δθgd2<−0.062  (21a)

To obtain still further sufficient correction of chromatic aberration,the range of the anomalous partial dispersion value Δθgd1 defined byconditional expression (21a) can be redefined as follows:

−0.5620<Δθgd2<−0.112  (21b)

To obtain further sufficient correction of chromatic aberration, theranges of the Abbe numbers νd1 and νd2 defined by conditionalexpressions (22) and (23) can be redefined as follows:

νd1<50  (22a)

νd2<50  (23a)

To obtain still further sufficient correction of chromatic aberration,the ranges of the Abbe numbers νd1 and νd2 defined by conditionalexpressions (22a) and (23a) can be redefined as follows:

νd1<45  (22b)

νd2<45  (23b)

To obtain yet still further sufficient correction of chromaticaberration, the ranges of the Abbe numbers νd1 and νd2 defined byconditional expressions (22b) and (23b) can be redefined as follows:

νd1<40  (22c)

νd2<40  (23c)

In the exemplary embodiments, the optical elements GNL1 and GL1 made ofan optical material that satisfies conditional expressions (18) and (19)is employed for a lens and a refractive layer provided on a lens of theoptical system. In addition, if the refractive surface composed of suchan optical material is aspherical, chromatic aberration flare, such asspherical aberration of color, can be corrected. Furthermore, if aninterface is formed between the optical element and air atmosphere orbetween the optical element and an optical material having a relativelylow index of refraction, the chromatic aberration can be relativelysignificantly changed by slightly changing the radius of curvature ofthe interface.

In addition, to obtain further sufficient correction of chromaticaberration, the range defined by conditional expression (25) can beredefined as follows:

(φ1a×ΔθgF1a/νd1a)/(φ2a×ΔθgF2a/νd2a)>0.9  (25a)

Exemplary embodiments in which an optical element composed of theoptical materials that satisfy conditional expressions (18) to (27) isemployed for an optical system that satisfies conditional expression(17) are described in detail next.

In these exemplary embodiments, a UV-curable resin 1, N-polyvinylcarbazole, or a mixture of a UV-curable resin 2 and TiO₂ fine particlesdispersed therein is used for an optical material that satisfiesconditional expressions (18), (20), and (22). A mixture of theUV-curable resin 2 and ITO fine particles dispersed therein or a mixtureof N-polyvinyl carbazole and ITO fine particles dispersed therein isused for an optical material that satisfies conditional expressions(19), (21), and (23) relating to the second optical element GL1.

An optical system for use in each of the exemplary embodiments is aphoto-taking lens system used in an image pickup apparatus, such as avideo camera, a digital camera, or a silver-halide film camera. In thecross-sectional views of lenses, an object is located on the left side(the front side), and an image plane is located on the right side (therear side).

In the case where the optical systems of the exemplary embodiments areused for projection lenses of, for example, projectors, a screen islocated on the left side, and an image to be projected is located on theright side.

In the cross-sectional views of lenses, “i” represents the order of alens group numbered from the object. “Li” represents an ith lens group.

In addition, “SP” represents an aperture stop. The aperture stop S isdisposed between the second lens group L2 and the third lens group L3.“IP” represents an image plane. When the optical system is used for aphoto-taking lens of a video camera or a digital still camera, animaging surface of a solid-state image pickup element (a photoelectricconversion element), such as a CCD sensor or a CMOS sensor, is disposedin the image plane IP. When the optical system is used for aphoto-taking lens of a silver-halide film camera, a light-sensitivesurface corresponding to the film surface is disposed in the image planeIP. “GNL1” and “GL1” represent the first and second optical elements,respectively.

In aberration diagrams, “d” and “g” represent the d-line and g-line,respectively. “ΔM” and “ΔS” represent the meridional image plane and thesagittal image plane, respectively. The chromatic aberration ofmagnification is represented using the g-line. “ω” denotes the halfangle of field. “Fno” denotes the F number.

According to a fourteenth exemplary embodiment, as shown in FIG. 28, anoptical system is a wide-angle lens (a retrofocus optical system) havinga focal length of 24 mm. The optical system includes a first lens groupL1 having a negative refractive power, a second lens group L2 having anegative refractive power, and a third lens group L3 having a positiverefractive power. When focusing is carried out, the second lens group L2and the third lens group L3 are moved along the light axis.

According to the present embodiment, the optical system includes a firstoptical element GNL1 composed of the UV-curable resin 1 and a secondoptical element GL1 composed of a mixture of the UV-curable resin 2 and14.2% by volume ITO fine particles dispersed therein. As shown in FIG.28, the first optical element GNL1 is a lens (layer) composed of theUV-curable resin 1. The second optical element GL1 is a lens (layer)composed of a mixture including ITO fine particles.

According to the fourteenth embodiment, the first optical element GNL1composed of the UV-curable resin 1 and having a positive refractivepower and the second optical element GL1 composed of a mixture includingITO fine particles and having a negative power are disposed on the imageside relative to the aperture stop SP, where, when the paraxial marginalray passes through the first optical element GNL1 and the second opticalelement GL1, the height of the paraxial marginal ray from the light axisis relatively large.

In addition, the first optical element GNL1 is in tight contact with thesecond optical element GL1. In this way, axial chromatic aberration andchromatic aberration of magnification are sufficiently corrected.

According to a fifteenth exemplary embodiment, as shown in FIG. 30, anoptical system is a wide-angle lens having a focal length of 24 mm. Theoptical system includes a first lens group L1 having a negativerefractive power, a second lens group L2 having a negative refractivepower, and a third lens group L3 having a positive refractive power.When focusing is carried out, the second lens group L2 and the thirdlens group L3 are moved along the light axis.

According to the present embodiment, the optical system includes a firstoptical element GNL1 composed of a mixture of the UV-curable resin 2 and20% by volume TiO₂ fine particles dispersed therein and a second opticalelement GL1 composed of a mixture of the UV-curable resin 2 and 20% byvolume ITO fine particles dispersed therein on the reduction siderelative to the point P. As shown in FIG. 30, the first optical elementGNL1 is a lens (layer) composed of the mixture including TiO₂ fineparticles. The second optical element GL1 is a lens (layer) composed ofa mixture including ITO fine particles.

According to the fifteenth embodiment, the first optical element GNL1composed of the mixture including TiO₂ fine particles and having apositive refractive power and the second optical element GL1 composed ofa mixture including ITO fine particles and having a negative power aredisposed on the image side relative to the aperture stop SP, where, whenthe paraxial marginal ray passes through the first optical element GNL1and the second optical element GL1, the height of the paraxial marginalray from the light axis is relatively large.

In addition, the first optical element GNL1 is in tight contact with thesecond optical element GL1. In this way, axial chromatic aberration andchromatic aberration of magnification are sufficiently corrected.

According to a sixteenth exemplary embodiment, as shown in FIG. 32, anoptical system is a wide-angle lens having a focal length of 14 mm. Theoptical system includes a first lens group L1 having a negativerefractive power, a second lens group L2 having a positive refractivepower, and a third lens group L3 having a positive refractive power.When focusing is carried out, the second lens group L2 and the thirdlens group L3 are moved along the light axis.

According to the present embodiment, the optical system includes a firstoptical element GNL1 composed of the UV-curable resin 1 and a secondoptical element GL1 composed of a mixture of the UV-curable resin 2 and5% by volume ITO fine particles dispersed therein on the reduction siderelative to the point P. As shown in FIG. 32, the first optical elementGNL1 is a lens (layer) composed of the UV-curable resin 1. The secondoptical element GL1 is a lens (layer) composed of a mixture includingITO fine particles.

According to the sixteenth embodiment, the first optical element GNL1composed of the UV-curable resin 1 and having a positive refractivepower and the second optical element GL1 composed of a mixture includingITO fine particles and having a negative power are disposed on the imageside relative to the aperture stop SP, where, when the paraxial marginalray passes through the first optical element GNL1 and the second opticalelement GL1, the height of the paraxial marginal ray from the light axisis relatively large.

In addition, the first optical element GNL1 is in tight contact with thesecond optical element GL1. The first optical element GNL1 and thesecond optical element GL1 are cemented between the lenses. In this way,axial chromatic aberration and chromatic aberration of magnification aresufficiently corrected.

According to a seventeenth exemplary embodiment, as shown in FIG. 34, anoptical system is a wide-angle lens having a focal length of 24 mm. Theoptical system includes a first lens group L1 having a negativerefractive power, a second lens group L2 having a negative refractivepower, and a third lens group L3 having a positive refractive power.When focusing is carried out, the second lens group L2 and the thirdlens group L3 are moved along the light axis.

According to the present embodiment, the optical system includes a firstoptical element GNL1 composed of the UV-curable resin 2 and 3% by volumeTiO₂ fine particles dispersed therein and a second optical element GL1composed of a mixture of N-polyvinyl carbazole and 10% by volume ITOfine particles dispersed therein disposed on the enlargement siderelative to the point P. As shown in FIG. 34, the first optical elementGNL1 is a lens (layer) composed of a mixture including TiO₂ fineparticles. The second optical element GL1 is a lens (layer) composed ofa mixture including ITO fine particles.

According to the seventeenth embodiment, the aspherical first opticalelement GNL1 composed of a mixture including TiO₂ fine particles andhaving a negative refractive power and the aspherical second opticalelement GL1 composed of a mixture including ITO fine particles andhaving a positive power are disposed on the enlargement side relative tothe aperture stop SP. In this way, chromatic aberration of magnificationis sufficiently corrected.

According to an eighteenth exemplary embodiment, as shown in FIG. 36, anoptical system is a wide-angle lens having a focal length of 14 mm. Theoptical system includes a first lens group L1 having a negativerefractive power, a second lens group L2 having a positive refractivepower, and a third lens group L3 having a positive refractive power.When focusing is carried out, the second lens group L2 and the thirdlens group L3 are moved along the light axis.

According to the present embodiment, the optical system includes asecond optical element GL1 composed of a mixture of N-polyvinylcarbazole and 10% by volume ITO fine particles dispersed therein and afirst optical element GNL1 composed of N-polyvinyl carbazole disposed onthe enlargement side relative to the point P.

In addition, the optical system includes a second first-optical elementGNL2 composed of the UV-curable resin 1 and a second second-opticalelement GL2 composed of a mixture of the UV-curable resin 2 and 5% byvolume ITO fine particles dispersed therein disposed on the reductionside relative to the point P. As shown in FIG. 36, the first opticalelement GNL1 is a lens (layer) composed of N-polyvinyl carbazole. Thesecond first-optical element GNL2 is a lens (layer) composed of theUV-curable resin 1. The second optical element GL1 and the secondsecond-optical element GL2 are layers composed of a mixture includingITO fine particles.

According to the eighteenth embodiment, the first optical element GNL1composed of N-polyvinyl carbazole and having a negative refractive powerand the second optical element GL1 composed of a mixture including ITOfine particles and having a positive power are disposed on theenlargement side relative to the aperture stop SP.

In addition, the optical system includes the second-first opticalelement GNL2 composed of the UV-curable resin 1 and having a positiverefractive power and the second second-optical element composed of amixture including ITO fine particles and having a negative refractivepower on the reduction side relative to the aperture stop SP, where apoint at which paraxial marginal ray passes the optical elements isrelatively high from the light axis. The first optical element GNL2 isin tight contact with the second optical element GL2. The second-firstoptical element GNL2 and the second-second optical element GL2 arecemented between the lenses. In this way, axial chromatic aberration andchromatic aberration of magnification are sufficiently corrected.

Particular values used in fourteenth to eighteenth numericalembodiments, which correspond to the fourteenth to eighteenth exemplaryembodiments, are described below. In the following numericalembodiments, i denotes the order of a surface numbered from the object.Ri denotes the radius of curvature of the ith optical surface (the ithsurface), and Di denotes a distance between the ith surface and the(i+1)th surface along the light axis.

Ni and vi denote the index of refraction and the Abbe number of amaterial of the ith optical element (excluding a lens (layer) composedof a resin, a material including TiO₂ fine particles dispersed therein,or a material including ITO fine particles dispersed therein) for thed-line, respectively. NGNLj and vGNLj denote the index of refraction andthe Abbe number of a material of a lens GNLj composed of a resin, amaterial including TiO₂ fine particles dispersed therein, or a materialincluding ITO fine particles dispersed therein for the d-line,respectively. Here, j=1, 2, . . . “f” denotes the focal length of anoptical system. “Fno” denotes the F number. “ω” denotes the half angleof field.

The shape of an aspherical surface is expressed by the followingequation:

${x(h)} = {\frac{\left( {1/r} \right)h^{2}}{1 + \sqrt{\left\{ {1 - {\left( {1 + k} \right)\left( {h/r^{2}} \right)}} \right\}}} + {B\; h^{4}} + {C\; h^{6}} + {D\; h^{8}} + {E\; h^{10}} + \ldots}$

where

X is an amount of displacement from the surface vertex in the light axisdirection,

h is a height from the light axis in a direction perpendicular to thelight axis,

r is the paraxial radius of curvature,

k is the conic constant, and

B, C, D, E, . . . are aspherical coefficients at respective orders.

In Table 9 and in each aspherical coefficient, “E±XX” means “×10^(±XX)”.

Table 7 shows the indices of refraction, the Abbe numbers, the relativepartial dispersions, and the refractive powers of the refractive opticalsystem portions GNL1 and GL1 for the d-line, g-line, C-line, and F-line,and values for conditional expression (17) in each numerical embodiment.Table 8 shows the indices of refraction, the Abbe numbers, and therelative partial dispersions of the UV-curable resin 2, ITO, and TiO₂for the d-line, g-line, C-line, and F-line. Table 9 shows the values ofthe refractive optical elements GNLj and GLj for conditional expression(25) in each numerical embodiment.

(Fourteenth Numerical Embodiment) f = 24.48 Fno = 2.86 2ω = 82.9° R1 =82.826 D1 = 3.49 N1 = 1.6200 ν1 = 60.3 R2 = 356.140 D2 = 0.15 R3 =52.319 D3 = 1.00 N2 = 1.8823 ν2 = 38.8 R4 = 19.042 D4 = 6.35 R5 = 23.018D5 = 2.93 N3 = 1.8549 ν3 = 24.6 R6 = 39.827 D6 = 3.93 R7 = 23.589 D7 =0.90 N4 = 1.8850 ν4 = 41.0 R8 = 11.029 D8 = 4.03 R9 = 67.716 D9 = 3.48N5 = 1.8653 ν5 = 28.6 R10 = −104.585 D10 = 1.90 R11 = −89.294 D11 = 6.00N6 = 1.5386 ν6 = 48.1 R12 = 100.213 D12 = 1.63 R13 = ∞ (Aperture Stop)D13 = 0.18 R14 = 41.507 D14 = 5.21 N7 = 1.8125 ν7 = 46.6 R15 = −21.714D15 = 3.25 R16 = −23.260 D16 = 3.00 N8 = 1.8539 ν8 = 24.2 R17 = 26.429D17 = 0.60 NGNL1 = 1.6356 νGNL1 = 22.7 R18 = 76.433 D18 = 0.05 NGL1 =1.5648 νGL1 = 20.0 R19 = 48.627 D19 = 1.27 R20 = −38.277 D20 = 1.92 N9 =1.6142 ν9 = 60.6 R21 = −18.636 D21 = 0.15 R22 = 447.518 D22 = 2.58 N10 =1.7800 ν10 = 50.0 R23 = −29.043

(Fifteenth Numerical Embodiment) f = 24.48 Fno = 2.86 2ω = 82.9° R1 =72.998 D1 = 3.78 N1 = 1.5959 ν1 = 61.6 R2 = 300.555 D2 = 0.15 R3 =44.538 D3 = 1.00 N2 = 1.8850 ν2 = 41.0 R4 = 16.752 D4 = 6.89 R5 = 18.821D5 = 2.85 N3 = 1.8500 ν3 = 23.0 R6 = 28.023 D6 = 4.09 R7 = 22.808 D7 =0.90 N4 = 1.8628 ν4 = 27.5 R8 = 11.104 D8 = 2.76 R9 = 65.695 D9 = 1.98N5 = 1.8551 ν5 = 24.6 R10 = −74.883 D10 = 0.25 R11 = −102.304 D11 = 7.35N6 = 1.5283 ν6 = 66.3 R12 = 52.340 D12 = 3.42 R13 = ∞ (Aperture Stop)D13 = 0.15 R14 = 37.044 D14 = 4.55 N7 = 1.8313 ν7 = 38.1 R15 = −20.625D15 = 2.34 R16 = −21.355 D16 = 5.02 N8 = 1.8500 ν8 = 23.0 R17 = 30.815D17 = 0.10 NGL1 = 1.5963 νGL1 = 13.9 R18 = 27.846 D18 = 0.30 NGNL1 =1.7088 νGNL1 = 21.6 R19 = 39.990 D19 = 1.18 R20 = −56.730 D20 = 2.18 N9= 1.4870 ν9 = 70.4 R21 = −17.915 D21 = 0.15 R22 = 10923.846 D22 = 2.60N10 = 1.7375 ν10 = 52.0 R23 = −26.864

(Sixteenth Numerical Embodiment) f = 14.36 Fno = 2.89 2ω = 112.8° R1 =48.138 D1 = 3.41 N1 = 1.7800 ν1 = 50.0 R2 = 29.278 D2 = 11.39 R3 =61.436 (Aspherical D3 = 7.51 N2 = 1.6762 ν2 = 55.7 R4 = 69.309 Surface)D4 = 0.15 R5 = 38.853 D5 = 1.80 N3 = 1.7800 ν3 = 50.0 R6 = 16.626 D6 =8.21 R7 = 85.187 D7 = 1.80 N4 = 1.7968 ν4 = 48.1 R8 = 19.176 D8 = 10.53R9 = 39.587 D9 = 2.00 N5 = 1.8027 ν5 = 47.5 R10 = 16.153 D10 = 7.00 N6 =1.7140 ν6 = 27.8 R11 = −212.616 D11 = 2.56 R12 = 92.281 D12 = 8.41 N7 =1.4870 ν7 = 70.4 R13 = −13.937 D13 = 1.20 N8 = 1.8500 ν8 = 23.0 R14 =−18.436 D14 = 4.50 R15 = −22.393 D15 = 1.20 N9 = 1.8850 ν9 = 41.0 R16 =−48.515 D16 = 1.00 R17 = ∞ (Aperture Stop) D17 = 1.00 R18 = 32.978 D18 =9.68 N10 = 1.8024 ν10 = 24.3 R19 = −20.944 D19 = 1.50 N11 = 1.8664 ν11 =29.1 R20 = 38.450 D20 = 0.92 R21 = −280.973 D21 = 1.20 N12 = 1.9230 ν12= 20.8 R22 = 22.614 D22 = 0.77 NGNL1 = 1.6356 νGNL1 = 22.7 R23 = 48.384D23 = 0.05 NGL1 = 1.5425 νGL1 = 29.0 R24 = 29.175 D24 = 3.89 N13 =1.4870 ν13 = 70.4 R25 = −22.037 D25 = 0.20 R26 = 56.727 D26 = 4.65 N14 =1.6236 ν14 = 60.0 R27 = −33.222 Aspherical Coefficient κ B C D E 3rdSurface 0.0000E+00 7.5524E−06 1.0025E−09 −4.2264E−12 8.3574E−15

(Seventeenth Numerical Embodiment) f = 24.48 Fno = 2.89 2ω = 82.9° R1 =59.261 D1 = 3.73 N1 = 1.6162 ν1 = 60.5 R2 = 168.165 D2 = 0.15 R3 =50.439 D3 = 1.00 N2 = 1.8850 ν2 = 41.0 R4 = 16.196 D4 = 9.20 R5 = 24.961D5 = 3.68 N3 = 1.8702 ν3 = 31.0 R6 = 91.548 (Aspherical D6 = 0.05 NGNL1= 1.5532 νGNL1 = 39.8 R7 = 36.183 Surface) D7 = 4.18 R8 = 27.255(Aspherical D8 = 0.36 NGL1 = 1.7127 νGL1 = 13.8 R9 = 40.419 Surface) D9= 0.90 N4 = 1.8771 ν4 = 35.0 R10 = 12.231 D10 = 2.24 R11 = 108.606 D11 =1.82 N5 = 1.8730 ν5 = 32.9 R12 = −61.248 D12 = 2.15 R13 = 274.153 D13 =5.81 N6 = 1.8623 ν6 = 27.3 R14 = 53.671 D14 = 2.41 R15 = ∞ (ApertureStop) D15 = 0.15 R16 = 40.484 D16 = 4.75 N7 = 1.8820 ν7 = 41.2 R17 =−21.289 D17 = 3.19 R18 = −25.560 D18 = 2.60 N8 = 1.8089 ν8 = 26.1 R19 =33.165 D19 = 1.13 R20 = −105.335 D20 = 2.15 N9 = 1.4870 ν9 = 70.4 R21 =−18.023 D21 = 0.15 R22 = −80.439 D22 = 2.20 N10 = 1.6180 ν10 = 60.4 R23= −22.171

(Eighteenth Numerical Embodiment) f = 14.35 Fno = 2.89 2ω = 112.8° R1 =54.598 D1 = 3.00 N1 = 1.7800 ν1 = 50.0 R2 = 31.238 D2 = 12.29 R3 =63.674 (Aspherical D3 = 7.47 N2 = 1.6406 ν2 = 58.4 R4 = 68.032 Surface)D4 = 0.80 NGL1 = 1.7127 νGL1 = 13.8 R5 = 79.476 D5 = 0.05 NGNL1 = 1.6959νGNL1 = 17.7 R6 = 68.330 D6 = 0.15 R7 = 39.761 D7 = 1.80 N3 = 1.7800 ν3= 50.0 R8 = 16.943 D8 = 7.75 R9 = 70.105 D9 = 1.80 N4 = 1.7800 ν4 = 50.0R10 = 18.934 D10 = 9.57 R11 = 43.123 D11 = 2.00 N5 = 1.8294 ν5 = 45.0R12 = 15.497 D12 = 7.00 N6 = 1.7549 ν6 = 26.0 R13 = −225.11 D13 = 2.65R14 = 105.224 D14 = 9.81 N7 = 1.4892 ν7 = 70.2 R15 = −13.547 D15 = 1.20N8 = 1.8500 ν8 = 23.0 R16 = −17.952 D16 = 4.55 R17 = −21.783 (ApertureStop) D17 = 1.20 N9 = 1.8850 ν9 = 41.0 R18 = −44.163 D18 = 1.00 R19 =0.000 D19 = 1.00 R20 = 25.752 D20 = 8.64 N10 = 1.6062 ν10 = 40.5 R21 =423.392 D21 = 1.26 N11 = 1.9230 ν11 = 20.8 R22 = 34.571 D22 = 0.98 R23 =−354.070 D23 = 1.20 N12 = 1.8821 ν12 = 38.6 R24 = 20.618 D24 = 0.64NGNL2 = 1.6356 νGNL2 = 22.7 R25 = 33.760 D25 = 0.05 NGL2 = 1.5425 νGL2 =29.0 R26 = 27.565 D26 = 3.81 N13 = 1.4870 ν13 = 70.4 R27 = −23.397 D27 =0.20 R28 = 53.7789 D28 = 4.67 N14 = 1.6532 ν14 = 57.4 R29 = −33.909Aspherical Coefficient k B C D E 3rd Surface 0.0000E+00 7.9984E−061.1075E−09 −4.1259E−12 8.5543E−15

TABLE 7 Fourteenth Embodiment Fifteenth Embodiment Sixteenth EmbodimentFirst Second First Second Optical Second Optical First Optical OpticalOptical Optical Element GNL1 Element GL1 Element GNL1 Element GL1Element GNL1 Element GL1 UV- 14.2% ITO - 20% TiO2 - 20% ITO - UV- 5%ITO - Conditional curable UV-curable UV-curable UV-curable curableUV-curable Expression resin 1 resin 2 resin 2 resin 2 resin 1 resin 2 Nd1.6356 1.5648 1.7088 1.5963 1.6356 1.5425 Ng 1.6753 1.5941 1.7599 1.63831.6753 1.5630 NC 1.6281 1.5544 1.7003 1.5804 1.6281 1.5362 NF 1.65601.5826 1.7331 1.6234 1.6560 1.5549 22, 23 νd 22.73 20.03 21.63 13.8622.73 29.05 θgd 1.4220 1.0517 1.5594 0.9761 1.4220 1.0963 θgF 0.68950.4197 0.8170 0.3459 0.6895 0.4346 20, 21 Δθgd 0.0826 −0.2996 0.2152−0.4049 0.0826 −0.2178 18, 19 ΔθgF 0.0652 −0.2147 0.1888 −0.3130 0.0652−0.1688 24 φ 0.0158 −0.0042 0.0078 −0.0020 0.0151 −0.0074 17 Lt/ft 3.7583.758 9.400 Eighteenth Embodiment Seventeenth Embodiment First FirstOptical Second Optical Second Optical Second Optical First OpticalElement Optical Element GNL1 Element GL1 Element GL1 Element GNL1 GNL2Element GL2 3% TiO2 - 10% ITO - N- 10% ITO - N- N- UV- 5% ITO -Conditional UV-curable polyvinyl polyvinyl polyvinyl curable UV-curableExpression resin 2 carbazole carbazole carbazole resin 1 resin 2 Nd1.5532 1.7127 1.7127 1.6959 1.6356 1.5425 Ng 1.5725 1.7772 1.7772 1.75161.6753 1.5630 NC 1.5494 1.6969 1.6969 1.6853 1.6281 1.5362 NF 1.56331.7483 1.7483 1.7246 1.6560 1.5549 22, 23 νd 39.81 13.85 13.85 17.6822.73 29.05 θgd 1.3852 1.2527 1.2527 1.4155 1.4220 1.0963 θgF 0.66450.5604 0.5604 0.6856 0.6869 0.4346 20, 21 Δθgd 0.1063 −0.1283 −0.12830.0533 0.0826 −0.2178 18, 19 ΔθgF 0.0898 −0.0986 −0.0986 0.0424 0.0652−0.1688 24 φ −0.0092 0.0086 0.0016 −0.0014 0.0122 −0.0036 17 Lt/ft 3.7579.406

TABLE 8 UV Curable Resin 2 ITO TiO2 Nd 1.5241 1.8571 2.3038 Ng 1.53711.9924 2.4568 NC 1.5212 1.7979 2.2803 NF 1.5313 1.9487 2.3745 νd 51.555.69 13.84 θgd 1.2695 0.8976 1.6241 θgF 0.5631 0.2901 0.8731

TABLE 9 Conditional Fourteenth Fifteenth Sixteenth Eighteenth ExpressionEmbodiment Embodiment Embodiment Embodiment ΔθgF1a × φ1a/νd1a 4.537E−056.817E−05 4.346E−05 3.510E−05 ΔθgF2a × φ2/νd2a 4.527E−05 4.599E−054.286E−05 2.092E−05 25 (ΔθgF1a × φ1a/νd1a)/ 1.002E+00 1.482E+001.014E+00 1.678E+00 (ΔθgF2a × φ2a/νd2a)

A digital still camera that includes one of the optical systemsaccording to the above-described exemplary embodiments as an imagingoptical system is described next with reference to FIG. 40.

As shown in FIG. 40, the digital still camera includes a camera body 20,an imaging optical system 21 according to one of the first to eighteenthexemplary embodiments, and a solid-state image pickup element (aphotoelectric conversion element) 22, such as a CCD sensor or a CMOSsensor. The solid-state image pickup element 22 is incorporated in thecamera body 20. The solid-state image pickup element 22 receives lightof an object image formed by the imaging optical system 21.

The digital still camera further includes a memory 23 and a finder 24.The memory 23 stores information about the object imagephoto-electrically converted by the solid-state image pickup element 22.The finder 24 includes, for example, a liquid crystal display panel. Thefinder 24 is used for viewing the object image formed on the solid-stateimage pickup element 22.

In this way, by applying one of the optical systems according to thepresent invention to a digital still camera, a compact optical apparatushaving high optical performance can be achieved.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all modifications, equivalent structures and functions.

This application claims the benefit of Japanese Application No.2006-326868 filed Dec. 4, 2006, No. 2007-035936 filed Feb. 16, 2007, andNo. 2007-137748 filed May 24, 2007, which are hereby incorporated byreference herein in their entirety.

1. An optical system comprising: a first optical element and a secondoptical element on at least one of an enlargement side and a reductionside relative to a point P at which a light axis and a paraxial chiefray intersect, each of the first optical element and the second opticalelement comprising a solid material having a refractive light incidentsurface and a refractive light emergent surface, wherein the followingconditional expressions are satisfied:ΔθgF1>0.0272,ΔθgF2<−0.0278, andf1×f2<0, where ΔθgF1 and ΔθgF2 denote anomalous partial dispersionvalues of the first optical element and the second optical element forthe Fraunhofer g-line and F-line, respectively, and f1 and f2 denotefocal lengths of the first optical element and the second opticalelement, respectively, when the light incident surfaces and the lightemergent surfaces of the first optical element and the second opticalelement are in contact with air.
 2. The optical system according toclaim 1, wherein the following conditional expressions are satisfied:Δθgd1>0.038, andΔθgd2<−0.037, where Δθgd1 and Δθgd2 denote anomalous partial dispersionvalues of the first optical element and the second optical element forthe Fraunhofer g-line and d-line, respectively.
 3. The optical systemaccording to claim 1, wherein the following conditional expressions aresatisfied:νd1<60, andνd2<60, where νd1 and νd2 denote Abbe numbers of the solid materials ofthe first optical element and the second optical element, respectively.4. The optical system according to claim 1, wherein the first opticalelement and the second optical element are disposed in the same lensgroup.
 5. The optical system according to claim 1, wherein at least oneof the surfaces of the first optical element and the second opticalelement is aspherical.
 6. The optical system according to claim 1,wherein at least one of the surfaces of the first optical element andthe second optical element is in contact with air.
 7. The optical systemaccording to claim 1, further comprising, in order from an object sideto an image side: a first lens group having a positive refractive power;a second lens group having a negative refractive power; an aperturestop; a third lens group having a positive refractive power; and afourth lens group having a positive refractive power, wherein theoptical system serves as a zoom lens, and distances between the firstthrough fourth lens groups are changed when zooming is performed, andwherein the first optical element and the second optical element areincluded in the first lens group.
 8. The optical system according toclaim 1, further comprising, in order from an object side to an imageside: a first lens group having a positive refractive power; an aperturestop; a second lens group having a negative refractive power; and athird lens group having a positive refractive power, wherein the firstlens group is stationary, the second lens group is movable along thelight axis, and the third lens group is stationary when focusing isperformed, and wherein the first optical element and the second opticalelement are included in the first lens group.
 9. The optical systemaccording to claim 1, further comprising, in order from an object sideto an image side: a first lens group having a negative refractive power;a second lens group having a negative refractive power; an aperturestop; and a third lens group having a positive refractive power, whereinthe first lens group is stationary, the second lens group is movablealong the light axis, and the third lens group is stationary whenfocusing is performed, and wherein the first optical element and thesecond optical element are included in the third lens group.
 10. Theoptical system according to claim 1, wherein the maximum height of aparaxial marginal ray from the light axis when the paraxial marginal raypasses through the lens surface on the enlargement side relative to thepoint P is greater than that on the reduction side relative to the pointP, and wherein the following conditional expression is satisfied:φ1×φ2<0, where φ1 and φ2 denote the refractive powers of the firstoptical element and the second optical element, respectively, when thelight incident and emergent surfaces of the first optical element andthe second optical element are in contact with air.
 11. The opticalsystem according to claim 10, wherein the following conditionalexpression is satisfied:Lt/ft<1.0, where ft denotes a focal length of the entire optical system,and Lt denotes a total lens length of the optical system.
 12. Theoptical system according to claim 10, wherein the first optical elementand the second optical element are disposed on the enlargement siderelative to the point P.
 13. The optical system according to claim 10,wherein the following conditional expressions are satisfied:φ1>0, andφ2<0.
 14. The optical system according to claim 10, wherein thefollowing conditional expression is satisfied:(φ1×ΔθgF1/νd1)/(φ2×ΔθgF2/νd2)<1.5, where νd1 and νd2 denote the Abbenumbers of the solid materials of the first optical element and thesecond optical element, respectively.
 15. The optical system accordingto claim 10, further comprising, in order from an object side to animage side: a first lens group having a positive refractive power; asecond lens group having a negative refractive power; and a third lensgroup having a positive refractive power, wherein the first lens groupis stationary, the second lens group is movable along the light axis,and the third lens group is stationary when focusing is performed, andwherein the first optical element and the second optical element areincluded in the first lens group.
 16. The optical system according toclaim 1, wherein the maximum height of a paraxial marginal ray from thelight axis when the paraxial marginal ray passes through the lenssurface on the enlargement side relative to the point P is less thanthat on the reduction side relative to the point P, and wherein thefollowing conditional expression is satisfied:φ1×φ2<0, where φ1 and φ2 denote refractive powers of the first opticalelement and the second optical element, respectively, when the lightincident and emergent surfaces of the first optical element and thesecond optical element are in contact with air.
 17. The optical systemaccording to claim 16, wherein the following conditional expression issatisfied:2<Lt/ft<15, where ft denotes a focal length of the entire opticalsystem, and Lt denotes a total lens length of the optical system. 18.The optical system according to claim 16, wherein the first opticalelement and the second optical element are disposed on the reductionside relative to the point P.
 19. The optical system according to claim16, wherein the following conditional expressions are satisfied:φ1a>0, andφ2a<0, where φ1a and φ2a denote refractive powers of the first opticalelement and the second optical element disposed on the reduction siderelative to the point P, respectively.
 20. The optical system accordingto claim 16, wherein the following conditional expression is satisfied:(φ1a×ΔθgF1a/νd1a)/(φ2a×ΔθgF2a/νd2a)>0.8, where φ1a and φ2a denoterefractive powers of the first optical element and the second opticalelement disposed on the reduction side relative to the point P,respectively, νd1a and νd2a denote the Abbe numbers of the materials ofthe first optical element and the second optical element, respectively,and ΔθgF1a and ΔθgF2a denote anomalous partial dispersion values of thefirst optical element and the second optical element for the g-line andF-line, respectively.
 21. The optical system according to claim 16,wherein the first optical element and the second optical element aredisposed on the enlargement side relative to the point P and aredisposed on the reduction side relative to the point P.
 22. The opticalsystem according to claim 16, wherein the following conditionalexpressions are satisfied:φ1b<0, andφ2b>0, where φ1b and φ2b denote the refractive powers of the firstoptical element and the second optical element disposed on theenlargement side relative to the point P, respectively.
 23. An opticalapparatus comprising: the optical system according to claim 1.